Comparing Oxygen Levels to Heart Rate Recovery and Peak Time

Contrasting Oxygen Levels with Heart Rate Recovery and Peak Time Examination Question How do various groupings of oxygen gave to the respiratory framework influence the pulse and in this way a subjectsâ athletic abilities? Presentation Right off the bat, it is critical to research how the bodys respiratory framework capacities. The lungs have two essential capacities, discharging carbon dioxide from the body and incorporating oxygen into the circulation system 3. The lungs never arrive at top limit and are not liable for the impediment in oxygen conveyed to the muscles 1. This is significant in light of the fact that, on account of this investigation the constraints might be reached. There is in every case around a similar measure of oxygen noticeable all around according to everything else: 21%. Howeverâ as elevation builds there is less pneumatic force and along these lines less oxygen accessible to the lungs per stomach compression cycle. Rather than changing the barometric weight, there will basically be less or more oxygen noticeable all around, in this trial. This may cause an anomalous outcome as the body reacts distinctively to definitely adjusted conditions. At the point when the oxygen substance of the a ir is definitely diminished, the blood will in all likelihood be essentially less soaked and when the oxygen substance of the air is radically expanded the blood ought to be increasingly immersed with oxygen 2. It is then important to explore how this may influence the cardiovascular framework. The measure of oxygen that is accessible to the cells while they are creating ATP to drive the body is significant, in such a case that there isn't sufficient oxygen accessible for vigorous breath, thanâ anaerobic breath will happen. Anaerobic breath will create lactate and carbon dioxide. The lactate (lactic corrosive), triggers a reaction from the thoughtful anxious system1, 2. The noradrenergic thoughtful sensory system produces norepinephrine. The SA hub (sinoatrial hub), animated by the norepinephrine hormone increments both the rate that the heart pulsates and how much the heart finishes a systolic compression 1,2. Notwithstanding the thoughtful sensory system, the medulla detects the expansion of carbon dioxide in the blood because of anaerobic breath. The medulla at that point imparts an electrical sign through the heart nerve to the SA node2. A live O2 machine will be utilized so as to complete this examination. It delivers and stores 15% oxygen and 95% oxygen independently. These will be the two convergences of oxygen that will be utilized to think about the occasions it takes for pulses to top and afterward recoup. The independantâ variable is the convergence of Oxygen. The dependantâ variable is the time it takes for the subject to top and the time it takes for the subject to recoup. The test will be constrained by controlling the speed at which the treadmill is set to. Since the purpose of this test is to analyze differencesâ the contrast in the people athletic capacity ought not have any kind of effect in the information. Materials Live O2 Machine Breathing apparatus Treadmill Pulse/oxygen immersion screen Clorox and paper towels Clock Exploratory Overview The Live O2 machine which will be utilized to make, store and convey the two distinct groupings of oxygen is contained an oxygen machine, stockpiling pack with two compartments, a conveyance framework with a veil and a change to change which convergence of oxygen is being conveyed. The image above, delineating the live O2 framework is the one that was utilized, aside from a treadmill was usedâ instead of a fixed bicycle as is portrayed. The guineas pigs pulse top occasions and recuperation times were first tried with the expanded degree of oxygen, they were then given a time of rest while another subject ran on the treadmill. At that point, after the time of rest the subject would run on the treadmill again and their pinnacle and recuperation times would be estimated with the limited degrees of oxygen. The edge for the pulse cresting was 140 bpm. The limit for recouped was the point at which the pulse of the subject was inside 10 of their unique resting pulse. For instance, if the guineas pigs resting pulse was 65 bpm, they would be viewed as recouped when their pulse dropped back underneath 75. Methodology Stage 1 First 8â willing individuals were discovered, who were physically fit enough that there would not be any harm to their body through the testing. At that point the 8â people were told not to drink such a caffeine or some other energizer before the trial. The veil of the live O2 machine was cleaned with cloroxâ and the oxygen machine was gone on to top off the two individual sacks. Stage 2 At that point the resting pulse of the subject was taken with the pulse screen. Ten was added to the resting number to decide the edge that the pulse must reach during recuperation to decide if the subject has recouped. The pulse screen was left on the subjectsâ finger to screen their pulse, Thenâ the oxygen was set to the 95% setting and the treadmill was set to 5 miles for each hour. At that point, when the subject was at 5 miles for every hour the clock was begun and the subject was instructedâ to hold the veil to their face. The clock was halted once the subjects pulse arrived at 140 bpm. At that point the treadmill was halted and the subject was told to keep the cover on. At that point the time it took for their pulse to come back to the foreordained resting rate was estimated. Stage 3 The primary subject was then given rest while subject 2 performed stage 2. When subject 2 was finished with stage 2, subject 1 rehashed stage 2 with 15% oxygen rather than 95% oxygen followed again by subject 2. The cover was cleaned with cloroxâ between each subject. Stage 4 Stages 1-3 were rehashed with the stayed of the guineas pigs and the information was recorded in a table inside the lab book. Security contemplations Since this lab works with the human body and estimating its reactions to what exactly could be consideredâ strenuous circumstances, there must be safeguards taken. Right off the bat, the entirety of the subjects that were tried, were either in acceptable or excellent state of being and had no prior wellbeing intricacies that would jeopardize them during the investigation. To additionally guarantee that there was no physical damage done to the subjects, the subjects immersion was continually observed with the pulse/oxygen immersion screen. In the event that anytime during the 15% oxygen test the immersion plunged excessively low (beneath 85% immersion) and stayed there for in excess of a few seconds then the 95% oxygen would promptly been turned on and that round of testing would be ended and the subject opportunity to rest. The veil that was being utilized was additionally continually cleaned with cloroxâ to forestall the spreading of germs. Investigation Subjective factors The two fundamental factors that may have influenced the information were: the pulse screen and the breathing apparatus. The way that the subject needed to hold the screen on their finger and the veil while running made the pulse screen marginally off base and now and then would just not take readings. It possibly worked when the subject was clutching it and this upset their typical running examples. A few subjects additionally experienced difficulty holding the cover to their face with enough power to hold a seal while running. This may have given a portion of the normal air access to the cover. Holding the veil additionally restrained the subjects normal running example. The way that the subjects common running example was repressed made it harder for them to keep an ordinary running pace even with the treadmill set at a steady 5 miles for every hour. Controlling these things without a moment's delay may have likewise included to the strain the subjects body, which could have influ enced the outcomes. At that point at long last, there is likewise the way that everybody that was being tried was diverse in their natural cosmetics and in this manner will react somewhat distinctively to the two convergences of oxygen. Information Complete Peak and Recovery times (in short order) run: 95% Oxygen Peak times (s) 95% Oxygen Recovery time (s) 15% Oxygen Peak times (s) 15% Oxygen Recovery time (s) 1 187 45 62 185 2 180 56 52 102 3 200 64 40 188 4 181 69 39 73 5 153 71 36 123 6 108 52 60 201 7 181 21 56 133 8 144 61 27 177 This table shows each run and the occasions in seconds related with it. The runs where the higher convergence of oxygen (95%) was utilized are shown first, on the left. The runs where the lower convergence of oxygen (15%) was utilized are shown second, on the right. The pinnacle times (the time it takes for the subjects pulse to arrive at 140 bpm from resting) are shown in the second and fourth section and the recuperation times (the time it takes for a subjects pulse to go from 140 bpm back to inside 10 of resting) are shown in the third and fifth segment. This visual chart shows the normal recuperation times and pinnacle times for the two distinct degrees of oxygen fixation. The recuperation times are recorded at the top and the pinnacle times are recorded at the base. Normal Difference in Peak and Recovery time like a flash Pinnacle time (s) Recuperation time (s) Distinction 120.25 92.875 This table shows the distinction between the normal pinnacle time of the 95% and 15% oxygen focus. Just as the contrast between the normal recuperation time of the 95% oxygen and the 15% oxygen focuses. Assessment Finish of results There is a reasonable contrast between the occasions for the two distinctive convergence of oxygen. At the point when the subject was regulated 95% oxygen their pinnacle times took a normal of 166.75 seconds, while when the normal pinnacle time when just 15% oxygen focus was directed was 46.5 seconds. This is a distinction of 120.25 seconds, so unmistakably when a subject is controlled more oxy

The Implications of Reconstruction Essay Example | Topics and Well Written Essays - 500 words

The Implications of Reconstruction - Essay Example 562). Remaking's greatest disappointment was the kickback that was made when Northern Republicans endeavored to lead the South. The kickback brought about brutal detest bunches that disturbed the political framework, and the lives of African-Americans for the following 100 years. The thirteenth, fourteenth, and fifteenth corrections were totally passed during the time of reproduction. These significant corrections denied subjection, ensured the liberated slaves citizenship, and allowed them the option to cast a ballot, however were to a great extent unenforceable in the South. In any case, these revisions would frame the establishment for the Civil Rights development 100 years after the fact. Reproduction finished when the contested appointment of 1876 saw the Republican Rutherford B Hayes gain the administration, despite the fact that the constituent votes were in debate. Consequently, Hayes consented to expel the bureaucratic soldiers from the South and not contradict the recently shaped Democratic governments there (Zuczek 171). This spelled a conclusion to Reconstruction and an additional 100 years of racial viciousness, isolation, and segregation. By the late nineteenth century, African-Americans had still not understood the American long for freedom and the option to cast a ballot, or the established ensures that accompanied the thirteenth, fourteenth, and fifteenth revisions.

The Play King Lear Essay Example For Students

The Play King Lear Essay Lord Lear depends on appearance and reality. The two dads in the fundamental plot and the subplot manage youngsters who beguile by appearances. Lear is taken by bogus words and appearances similarly as Gloucester seems to be. Add to this few characters in the play seem, by all accounts, to be somebody however they end up being others, for example, Edgar masked as a poor person and Kent camouflaged as a hireling. What concerns the simpleton, he has all the earmarks of being silly yet in all actuality he is astute. Goneril and Regan are the embodiment of lip service. Goneril misrepresents, by attempting to trick her dad and state that her adoration is insufficient contrasted with his. The expression An adoration that makes breath poor and discourse unfit demonstrate it. She attempts to cause her affection to appear to be extremely valuable. Then again, Regan is no less. Regan discloses to her dad that her own pleasure lies exclusively in the satisfaction in his adoration. The sisters love is an unfortunate obligation. We will compose a custom exposition on The Play King Lear explicitly for you for just $16.38 $13.9/page Request now Reality lies behind appearance when Goneril and Regan comment about their dad toward the finish of the scene on the sickness old enough. They gripe about Lears rash judgment and unexplainable conduct and they are uneasy that they will get a similar treatment of Codelia thus they settle that they, must accomplish something, and Ith heat. Appearance and reality affect King Lear. Goneril is weary of her dad as she blames him that because of his character the knights are acting in a grievous manner, and recommends that disciplinary measures must be taken. Lear is stunned as he answers her, Are you our little girl?. Lear fakes it, as a methods for communicating his shock and amazement and these are indications of frenzy. The expressions, Does any here know me? This isn't Lear/Does Lear walk this? Talk this Where are his eyes? shows a King Lear who is getting powerless in his detects. He reviles Goneril and says that he despite everything has one kind and agreeable girl left to go to (Regan), yet she ends up being made of a similar stuff. She advises him to diminish the knights yet for Lear, they are an image of status. The ruler assaults and reviles his little girl to bring forth a difficult youngster that will torment her as his own jerk way of life as a lord. The man is utilized to honeyed words and her thoughtlessness is harming him. For Lear Kent in the stocks is an affront. At the point when Kent reveals to Lear that Your child and little girl in reference to the ones that put him there, Lear will not accept that Cornwall and Regan are answerable for his workers disgrace. Lear won't see reality. Lear is generally worried about his own psychological state as he fears he is getting crazy with distress. He is influenced genuinely as though his girls are assaulting him for within. Lear is stunned when he finds that Regan sides with her sister as she reveals to him that in the event that she checks his knights there are valid justifications. Regan advises Lear to follow Goneril with half of his knights and afterward he can come in her home. From each one of those expanded discourses, Lear anticipates benevolence and regard however Goneril doesn't need, not by any means the fifty knights. The expression, I gave all of you said by Lear shows biterness as it is a reality that hits him hard. For the many, Cordelia may have all the earmarks of being cool, ill bred, as though she needs to challenge her dad as she neglects to satisfy him since she will not partake in what one can say, an affection challenge. She says she has nothing to state as she lets him know, What will Cordelia talk cherish and be quiet. However, in actuality she is the encapsulation of a caring girl and one can secure this, on the grounds that the lord of France says that he takes her since she is a lady of honesty. Yet her dad has ousted her from the realm, Cordelia is extremely miserable when she read the letters, depicting Lears treatment on account of her sisters. One can see that blessed water tumbled from her wonderful eyes as she regretted Lears situation. Cordelia shows that her adoration is to an end when she sends her warriors to scan for Lear, who is as yet meandering outside as she feels sorry for and feels for him. She shows a profound real worry for her dad. Equivalent to Edgar, she helps the parent who dismissed her so unfeelingly. In act four scene seven, Cordelia puts forth a valiant effort to reestablish her dad to rational soundness as she thinks about him through affection. Cordelia is feeling frustrated about her dad. She guides her identifies towards him. At the point when her dad discloses to her that in the event that she has any toxic substance he will drink I,t she answers, No reason, no reason concerning Cordelia, there is no motivation behind why she shouldnt deal with her dad, in light of the fact that Cordelia truly is a lady of standards and trustworthiness. .u4227b43f6e0e675360653c6c518db4bc , .u4227b43f6e0e675360653c6c518db4bc .postImageUrl , .u4227b43f6e0e675360653c6c518db4bc .focused content zone { min-tallness: 80px; position: relative; } .u4227b43f6e0e675360653c6c518db4bc , .u4227b43f6e0e675360653c6c518db4bc:hover , .u4227b43f6e0e675360653c6c518db4bc:visited , .u4227b43f6e0e675360653c6c518db4bc:active { border:0!important; } .u4227b43f6e0e675360653c6c518db4bc .clearfix:after { content: ; show: table; clear: both; } .u4227b43f6e0e675360653c6c518db4bc { show: square; progress: foundation shading 250ms; webkit-change: foundation shading 250ms; width: 100%; darkness: 1; change: obscurity 250ms; webkit-progress: mistiness 250ms; foundation shading: #95A5A6; } .u4227b43f6e0e675360653c6c518db4bc:active , .u4227b43f6e0e675360653c6c518db4bc:hover { haziness: 1; progress: murkiness 250ms; webkit-progress: murkiness 250ms; foundation shading: #2C3E50; } .u4227b43f6e0e675360653c6c518db4bc .focused content territory { width: 100%; position: rel ative; } .u4227b43f6e0e675360653c6c518db4bc .ctaText { fringe base: 0 strong #fff; shading: #2980B9; text dimension: 16px; textual style weight: striking; edge: 0; cushioning: 0; content enhancement: underline; } .u4227b43f6e0e675360653c6c518db4bc .postTitle { shading: #FFFFFF; text dimension: 16px; textual style weight: 600; edge: 0; cushioning: 0; width: 100%; } .u4227b43f6e0e675360653c6c518db4bc .ctaButton { foundation shading: #7F8C8D!important; shading: #2980B9; outskirt: none; outskirt range: 3px; box-shadow: none; text dimension: 14px; textual style weight: intense; line-stature: 26px; moz-fringe sweep: 3px; content adjust: focus; content adornment: none; content shadow: none; width: 80px; min-stature: 80px; foundation: url(https://artscolumbia.org/wp-content/modules/intelly-related-posts/resources/pictures/straightforward arrow.png)no-rehash; position: outright; right: 0; top: 0; } .u4227b43f6e0e675360653c6c518db4bc:hover .ctaButton { foundation shading: #34495E!important; } .u4227b43f6e0e675360653c6c518db4bc .focused content { show: table; tallness: 80px; cushioning left: 18px; top: 0; } .u4227b43f6e0e675360653c6c518db4bc-content { show: table-cell; edge: 0; cushioning: 0; cushioning right: 108px; position: relative; vertical-adjust: center; width: 100%; } .u4227b43f6e0e675360653c6c518db4bc:after { content: ; show: square; clear: both; } READ: Drama play audit EssayOne can draw up a parallelism between the primary plot and the subplot on what concerns appearance and reality. Gloucester is taken by bogus words and appearances, similarly as Lear seems to be. In the two plots the guiltless and adorable youngster is pushed off and the dad guarantees his properties to the disgraceful kids, as a byproduct of a demonstration of fondness. The shrewd kids make progress. Since Edmund is the charlatan child, he has no rights on the terrains. Like Goneril and Regan, Edmund is prepared to guard his own advantages as he is set up to do anything seen from the expression, If Ill not take it with birth, Ill take the land by with. He composes a letter which is evidently from Edgar where there is composed that Edgar looks for his Gloucesters life. He imagines he doesnt need to show to his dad, what he composed. With his dad, Edmund acts in a route and with his sibling in another manner. For Gloucester, Edgar shows up the scalawag however his this is unexpected since Edmund is the scoundrel. He shows dazzle trust in Edmund much that he consents to let Edmund find reality on his siblings sentiments. Basically, Gloucester places himself in his children power. Edmund claims to be worried about family respects, attempts to show how faithful he is, the point at which he uses such words as equity to the reason. Various incongruities are seen for example, when Cornwa ll tells Edmund, I hear you have demonstrated your dad a kid like office and when he says Nature of this trust we will require yet this is unexpected as he isn't dependable. In act two scene one Gloucester acclaims Edmund as a devoted and common kid and this shows he acknowledges Edmund as his solitary authentic kid. Edmund doesn't just focus on Edgars legacy however thus to his dads title. We see that appearance lies behind reality when in act three scene five, Edmund betrays his dad. He doesn't show to Cornwall that he abhors his dad however he needs to demonstrate to Cornwall, that he is faithful to the nation and simultaneously dedicated to his blood. Edmund betrays his parent, his own fragile living creature and blood. Cornwall is given the letter which contains the data about the French attack as Edmund demonstrates his dad he is a government operative of France. It on account of Edmund that Cornwall expects to rebuff Gloucester for his injustice. He claims to be grieved that he has found his dad however he trusts he will discover his dad with Lear to make Cornwall considerably progressively dubious. The thought of appearance and reality can be examined from Edgars perspective as he camouflages himself as a distraught hobo, Poor Tom. Edgars camouflage influences the lord and the plot. At the point when Edgar shows up as Poor Tom, Lear is persuaded that savage little girls probably diminished this forsaken man to beggary. Edgar needs to give a valiant effort to be persuading as a lunatic. In Lears eyes Edgar is the unaccommodated man as he considers Edgar to be a poor, exposed, forked creature. Lear feels that is just somebody like poor Tom who has nothing unnecessary (far beyond) that can train him on the essenti

Evolution Of Main Cgaracter in Song of Solomon - Free Essay Example

  When we think about coming of age, we not only focus on transition, we focus on the growth a person has overcome in a certain amount of time. In the book Song of Solomon, Toni Morrison captures the term with one of the main protagonists; Milkman Dead. Initially, you may automatically get the idea that Milkman is selfish and self centered. With this idea the author brings us along on Milkmans journey when he decides to find himself and learn more about his familys past. We see how this process has affected him socially and personally in how he came of age.   Milkmans background is what makes his character in the beginning so essential to his transition. Milkman comes from a wealthy background, with his mother being the daughter of a famous black doctor and his father being a wealthy landlord. Even though the family is wealthy, doesnt mean that they are a great, well put together family. When reading the beginning, you get the idea that their family is dysfunctional, and this has an effect on milkman. As a kid milkman was isolated from everyone else. Hed never played like that as a child. As soon as he got off his knees at the window sill , grieving because he could not fly, and went off to school, his velvet suit separated him from the other children (Morrison 264). His money and his lifestyle separated him from other kids, which caused him to not have any friends. Because of this Milkman mostly stuck around his father and thats where he was tied down to the family legacy. Milkmans father, Macon Dead was a cold man, who only cared ab out himself and money. Through the years of milkmans childhood, this behavior rubs off him and thats where Milkmans behavior changes. Milkman never respected the women in his life throughout the first part of the book, especially the women in his own family. He emulated his father by not listening to the needs of a woman, and also ignoring the wisdom they have. Pilate was the main women who provided wisdom to milkman about the respect of women, even though it wasnt directly thrown at him. When Reba was getting beat up by her lover in chapter 4, Pilate stepped up and made it be known that no women should be disrespected by a man. Although Milkman witnessed it all he still learned nothing considering the fact that he treats women as if they were nothing. He grows disrespecting women and Magdalene Lena, his older sister, finally stepped up and said something to him about it. When milkman decides to tell his father about the secret relationship his other sister Corinthians had with a tenant named Porter, his father immediately makes her end it because porter was poor, and this triggered the fight scene between Milkman and Lena. Lena points out the time where Milkman peed on her when they were kids and Milkman is left confused wondering why Lena had brought it up. She relates this memory in the past to the way Milkman treats women now and this makes Milkman think. Youve been laughing at us all your life. Corinthians. Mama. Me. Using us, ordering us, and judging us: how we cook your food; how we keep your house(Morrison 215). Lena was tired of Milkman taking advantage and using women for his own benefit. Even though this was Lenas only scene in the book, it is an important one because it set its mark as the climax in the book where Milkman learns that is actions always affects people even the one he has close to him. You are to blame. You are a sad, pitiful, stupid, selfish, hateful man. I hope your little hogs gut stands you in good stead, and that you take good care of it, because you dont have anything else. But I want to give you notice. She pulled her glasses out of her pocket and put them on. Her eyes doubled in size behind the lenses and were very pale and cold. I dont make roses anymore, and you have pissed your last in this house(Morrison 216). Milkman perspective on women changes towards the ending of the book. When Hagar dies, who was Milkmans ex lover, Milkman comes to his senses and thought that is was wrong that he used her when all she did was love him.

Essay on Prevention of Animal Overpopulation - 1722 Words

Countless lives locked away in cages and forgotten about have overwhelmed our society, it has left blood stains on our history as a species and if history has taught us anything, it’s that we have a choice to change our ways of adjusting to situations. A war which was fought in pursuit of ending such criminal means, yet we as human beings do little to nothing to end the horrific crimes of animal deaths in shelters. It is no secret that this world has become infused with problems that have extended from one side of the globe to the other. Amongst these problems lies a terrible truth: nearly every year, sums of almost eight million cats and dogs have been placed in shelters around the world. Out of these vast numbers, half will be†¦show more content†¦Impacting these numbers were combining cat and dog statistics, participation in rescues and enormous numbers of incoming dogs and cats (WV Animal Shelter Euthanasia Rates) despite the passing of animal life, there is still hope in saving them now. There are many ways for us to help prevent overpopulation in animals, however, the most effective way is to just spay or neuter. Spaying and neutering is basically removing the reproductive organs of an animal so that it won’t be able to produce any offspring. Of course with every new concept in life, a series of doubts and concerns are met, in this particular case: myths. 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Pollution is changing the atmosphere much sooner than expected and global warming is predicted to overwhelm the atmosphere within the next half of a century. In order to sustain the environment and atmosphere humans must take immediate action right now. The longer we wait to start immediate prevention, the sooner our air and water supplies will diminishRead MoreBenefit Of Technology Essay1023 Words   |  5 Pagesthis argument, resulting in a clear and supported argument. Technology has a catastrophic effect on multiple aspects of h umankind, but for the purpose of keeping this essay condensed and informative, only three will be discussed. These consist of overpopulation, the negative effects on both the environment and society. When analyzing the benefits of technology one of the areas that most people point to is medicine. The advances in the medicine field has allowed for people to live longer than ever, healing

Analysis Of Dungeons And Dragons Remake - 2323 Words

Dungeons and Dragons remake Okita, Gozen Shiing! My sword sings as I pull it from my sheath, instantly making me feel like its fate to feed my sword blood again. I slide it across my pointer and middle fingers of my left hand, steadily watching my reflection. I take a deep breathe and kick the door down to the queen consort s chambers. Damn, they ve already been here.... now it s a game of chase. I smirk to this conclusion I ve come to. I jump out the window and study my surroundings, only to realize I ve jumped into a new world. Wait... a new..... world? I look behind me at the window. Back in my world I was a famous Samurai that killed the king and took his place. I say famous, which is true, but only for my lust of blood. I am a fantastic fighter (sword and hand-to-hand), I am wearing somewhat decent armour, and I have a few things of value I could trade if needed. Deaths don t bother me. Do I resume chase here, or go back to the castle and look? Armour- +60 Weapong- Katana sword, dagger Money- $100 Skills: Sword fighting, hand-to-hand, can handle a combat dying (is that a good or bad thing?), I am very athletic. faults: I get mad easily and it sometimes causes me to make the wrong decision. Eward R. Halwell I tap my fingers on my desk while leaning on my right hand. I let slide a yawn, only to realized Mr. Owren s face. I m sorry, Mr. Halwell. Am I boring you? This is of great importance. Hey says trying to keep his compsure, only to fail. I lookShow MoreRelatedThe Role Of Playing Game ( Frpg ) Or Dungeons Dragons ( Dnd )2699 Words   |  11 PagesWhen you hear the words Fantasy Role Playing Game (FRPG) or Dungeons Dragons (DnD) there is a certain level of nurtured bias that is applied to the people who are interested in these things. If you were to paint a picture of someone who plays this type of thing I’m sure that person would have glasses, be overweight, and probably have difficulty socializing as a normal person. However, you might also see those same people as having above average intelligence and probably have a good job. The stereotypes

Teaching in Nursing A Guide for Faculty

Question: Do you believe the proposal would be approved if formally proposed? What are some strengths and weaknesses of the proposal? Answer: Nursing programs allow nursing students to have patient contact while learning about nursing skills in the classroom (Billings Halstead, 2013). Such programs allow the students to gain experience and gather valuable knowledge in different areas of nursing that are beneficial for them in the future in due course of their nursing practice (Keating, 2014). The programs teach students to function as a part of the medical team and give patient care to a diverse population of patients (Kable et al., 2013). There is a need for funding more such programs so that the quality of patient care becomes more advanced and of high quality. Such a nursing program is hereby presented to the board for funding approval. The title of the program is Nursing Quality and Performance Improvement Program. This executive summary of the program includes the purpose of the project, the target population, the benefits of the program, the cost justification and the basis of evaluation of the program. The purpose of the program Nurses involvement is very much crucial in health care improvement initiative (Hamric et al., 2013). The Nursing Quality and Performance Improvement Program establishes a framework for placing nurses on the frontline of transforming healthcare by high quality nursing practice. The program takes into consideration that ensures highly effective and reliable personalized care with the contributions and capabilities of the entire nursing team. The purpose of the program are as follows: Safety- nurses are able to avoid injuries to patients from the care given for helping them. Effective- nurses are able to provide services to the patients based on scientific evidence who can benefit to a great extent Patient-centered- nurses are able to provide to care that is responsive to and respectful of patient preferences, values and needs and ensures that the patient values are considered in the clinical decisions Timely- nurses are able to reduce wait times and potentially harmful delays for those who give and receive care Efficient- nurses are able to avoid waste of supplies, equipment, and human resources Equitable- nurses are able to provide care equitable in quality because of characteristics like gender, age, ethnicity and socioeconomic status (Ouslander et al., 2014). The program would focus on some particular goals. It would focus on transformational leadership of nursing. It would help to redesign care to optimize professional knowledge and expertise of the nurses. It would engage the nurses to work with members of the nursing team in the healthcare sector for ensuring reliable and safe care. Nurses would build system and culture of safety encouraging and supporting teamwork and vitality in all aspects of nursing. Nurses would be more knowledgeable about the processes and structures ensuring patient centered care. A quality learning system would be used up so that nurses get access to feedback and measurement about innovative care delivery (Oshiro et al., 2013). The target population The program would be set for final year nursing students. Such programs are highly beneficial for final year nursing students as they are to become a part of a healthcare setting in a short span of time. Sufficient training makes sure that the nurses are able to deliver proper care to the patients when they join a health care seting. The benefits of the program On completion of the program, the nurse would be able to develop the skills and knowledge required for delivering high quality patient care. They would be able to develop transformational leadership in themselves who would be able to create and implement an environment for meeting patient needs. The program would empower and engage nurses to act as leaders in ensuring high quality patient care. Organizational learning opportunities would be provided for the nurses to work in teams. The program would develop care systems that would support nurse workflow for optimizing patient and nurse interaction. It would provide the opportunity for the achievement of all measure targets and regulatory standards. Reduction of hospital-acquired conditions would be another benefit from the program (Nadeem et al., 2013). The cost justification The program needs funding for providing resources to the nurses taking part in the program. The main cost would involve preparing study materials and notes for the participants. Sufficient funding would make sure that all participants are provided with adequate resources and sufficient time for participation. It would be highly advantageous to the program if it is fully funded and the participants are thereby encouraged to bring positive changes in their nursing practice. The basis upon which the program will be evaluated The program would be evaluated by conducting a written examination for the participants. It would be conducted a month after the completion of the program. The aim would be to assess and evaluate the propagation of the knowledge aimed at imparting to the students. The nurses would be adjudged on the knowledge of the following points: nursing leadership, patient safety, risk management, patient care, team work, team collaboration, communication. Nurses must be able to participate in shared governance and improvement initiatives and adhere to evidence based policies and protocols. They must be able to be responsible for the delivery of effective and safe patient care and have the knowledge for actively participating in safety and quality of the patients. They must be responsible for proper identification and reporting of adverse effects that may rise in healthcare settings and participate in the design of safe processes (Panzer et al., 2013). References Billings, D. M., Halstead, J. A. (2013).Teaching in nursing: A guide for faculty. Elsevier Health Sciences. Hamric, A. B., Hanson, C. M., Tracy, M. F., O'Grady, E. T. (2013).Advanced practice nursing: An integrative approach. Elsevier Health Sciences. Kable, A. K., Arthur, C., Levett Jones, T., Reid Searl, K. (2013). Student evaluation of simulation in undergraduate nursing programs in Australia using quality indicators.Nursing health sciences,15(2), 235-243. Keating, S. B. (2014).Curriculum development and evaluation in nursing. Springer Publishing Company. Nadeem, E., Olin, S. S., Hill, L. C., Hoagwood, K. E., Horwitz, S. M. (2013). Understanding the components of quality improvement collaboratives: a systematic literature review.Milbank Quarterly,91(2), 354-394. Oshiro, B., Kowalewski, L., Sappenfield, W., Alter, C., Bettegowda, V., Russell, R. et al. (2013). A Multistate Quality Improvement Program to Decrease Elective Deliveries Before 39 Weeks of Gestation.Obstetrics Gynecology,121(5), 1025-1031. https://dx.doi.org/10.1097/aog.0b013e31828ca096 Ouslander, J. G., Bonner, A., Herndon, L., Shutes, J. (2014). The Interventions to Reduce Acute Care Transfers (INTERACT) quality improvement program: An overview for medical directors and primary care clinicians in long term care.Journal of the American Medical Directors Association,15(3), 162-170. Panzer, R. J., Gitomer, R. S., Greene, W. H., Webster, P. R., Landry, K. R., Riccobono, C. A. (2013). Increasing demands for quality measurement.JAMA,310(18), 1971-1980.

Structure of the Buying Center free essay sample

In addition to all the factors studied before, our framework contains a new construct, the environmental characteristics, which has not been studied before by other researchers. Within each construct we added some new characteristics and we eliminated the duplications. Key words: buying center; purchasing management; organizational behavior. Literature review The buying center notion has been one of the most important conceptual contributions made in the study of organizational buying behavior. The concept of the buying center refers to all those members of an organization who become involved in the buying process for a particular product or service (Robinson et. al 1967). The main research streams of investigation found in literature include: buying center structure and factors that influence it; influence of members of the buying center; and communication between members of the buying center. Most researchers have studied the changes in the buying center (BC) composition and structure over the buying process and the factors that determined these changes. We will write a custom essay sample on Structure of the Buying Center or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Researchers that studied the factors that determine changes in the BC composition and structure found four main categories of factors that influence the BC structure: company specific characteristics, purchase related characteristics, participants characteristics and type of the decision. A list of all factors that have been researched and the author(s) that has/have studied them is given in Table 1. From all these characteristics, purchase or product characteristics were found to be the most influential upon the structure of the buying center.

Taxation in the United States

Taxation in the United States Introduction Payments of taxes in the US are made up of four levels, which can make the whole system a complex matter. The tax code of the US is possibly the most composite compared with other countries, and each day the Congress includes additional pages for tax regulation. These four levels normally include federal government, state government, regional government and local government (Economicwatch.com).Advertising We will write a custom report sample on Taxation in the United States specifically for you for only $16.05 $11/page Learn More The forms of tax levied at every government level vary partly as a result of constitutional restrictions; income tax, for instance, is levied at state and federal government levels. Property taxes are normally levied only at local government level, though there might be numerous local jurisdictions which levy similar properties. Various state governments as well as federal government impose excise taxes while the local and state governments impose sales taxes, it is only the federal government that imposes the tariffs or custom duties (Economicwatch.com). Other various taxes like the licence fees are also imposed (Economicwatch.com). Taxes are normally levied on the natural persons (individuals), estates, business entities, trusts or any other types of organization. US taxes are based on income, property, business activity, importation of products, transactions, or other things and are normally levied on the relevant taxpayer for whom these factors are relevant. For instance, property owners are levied property taxes, individuals and business activities are levied income taxes; with some exceptions, one government level cannot impose taxes on the other government level. The subsequent section of this paper will focus on the US’s Federal taxation. Historical overview of taxation in US Ever since 1862 disbursing income tax to the federal government was made compulsory in the US. This was impo rtant in order to fund Civil War during that time, all the income level above $600 was taxed at a 3% income tax rate and a 5% tax rate was taxed in case the income was more than $10,000 (Economicwatch.com). But these rates were amended in 1864, and in the fiscal year 1895 the Supreme Court changed property taxes and affirmed that any income from the property would be taxed. Currently, a range of Federal government activities are financed by income earned from personal and corporate income taxes. In the past, these activities were funded by tariffs, but presently tariffs play an irrelevant role in offering financial support for the Federal government activities (Economicwatch.com).Advertising Looking for report on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More Tax code There is a tax code in the US’s taxation that is commonly called Internal Revenue Code of 1986; the main objective of this code is to coll ect revenues. In addition, the code is used to fulfil the social, economic and political objectives of the Federal government (Economicwatch.com). Tax progressivity The taxation system in the US is progressive, this means that as income increases the tax also increases meaning the taxpayer with superior income pays huge amount of taxes as well as superior tax rates. For instance, an individual earning $120,000 per year may pay 25% of his/her income as tax ($30,000 as total tax per year), while another individual earning $50,000 per annum may only pay at rate of 10% ($5,000 as tax per year) (Roach 11). The system of tax may also be proportional or regressive; a regressive system of tax is one when the tax paid decreases and an individual income increases at the same time; a proportional system of tax means that all taxpayers pay equal tax rate in spite of their income level (Roach 11). There are a number of reasons why the government uses progressive system of tax. First, this system represents an idea that those having high incomes must pay more taxes as a result of their superior capability to pay taxes without any crucial sacrifices. Second, the system addresses some economic inequalities existing in the society. The inequality is lessened through the use of high tax rate for those individuals with high income levels and a lower rate for those with low income levels (Roach 12). Finally, the system of progressive tax may yield a certain public income level with the smallest amount of economic impact. For instance, if there is a tax cut of $100, the individuals with low income may spend the whole amount in purchasing services and goods while the high income earners may spend a proportion of the $100 on services and goods and invest or save the rest. The saved or invested amount does not include additional demand level for services or goods in the economy. Thus, collecting more taxes from high earners maintains a superior and effective demand as well as more ac tivity in the economy (Roach 12). Residency status In order to file tax return in the US an individual must determine whether he/she is a non-resident or resident for tax purposes. Thus, if an individual is a non-resident and resident in one year, he/she is an alien with dual status, which means special rules are applied.Advertising We will write a custom report sample on Taxation in the United States specifically for you for only $16.05 $11/page Learn More The description of a resident for the purpose of taxes is completely different from the immigration status; this is because one may qualify to be a resident for the purpose of taxes, but still remain to be an alien for immigration purposes (Carter 1). A non-resident files a particular tax form and pays the tax only on the income earned in the US and he/she is subjected to particular rates where one may qualify for the treaty exemptions. On the other hand, US residents for the purpose of taxes are subject ed to similar rules and thus file similar forms as US citizens. This means that the worldwide income is reported instead of just incomes from the US sources (Carter 1). The US has treaties on the income tax with various foreign nations. In these treaties, foreign nations’ citizens resident in the US are levied at a lower rate or may be exempted from the income taxes of the US on specific items of the income they earn from sources. These decreased rates as well as exemptions differ amongst the nations and particular items of the income. In case a specific type of income is not covered by the treaty, or there exists no treaty between one nation and the US, the individual should pay tax on his/her income in similar manner and similar rate as shown in Form 1040NR’s instructions. Treaties on taxes decrease the tax paid by the foreign nations’ citizens resident in US; with specific exceptions, these treaties do not decrease taxes levied on the residents or US citizens (Unclefed.com). Advantages and disadvantages The benefits of levying tax on income are several; Individuals are levied depending on their total earnings, therefore individuals who earn less in theory pay a smaller amount of tax on their earnings. Individuals do not consume at equal rate, thus tax on incomes is an equitable manner of evaluating tax compared with the consumption tax. Individuals with lower levels of earnings would be mainly affected by direct tax on the consumption, because even essential things such as motor vehicles would considerably be more expensive. Earnings are a simple way to impose taxes as well as decide deductions. Whilst individuals may contend with a small number of pay stumps they ought to save, in the consumption tax, individuals may save the receipts for each acquisition they made throughout the year so as to qualify for tax breaks (Wisegeek.com). On the other hand, taxation disadvantages include; first, the tax collection on the income is mainly th ought to be harder than consumption tax that would be taxed at particular sale’s point. Second, taxation on income puts the lower class and middle class individuals on financial hardship, in spite of the total amount of income.Advertising Looking for report on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More Third, some individuals deem that the tax on the income is an infringement of the individual freedom of citizens. Particularly Libertarians contend that income tax infringes the right of the individual to make a decision on how to utilize the money that one receives. Finally, individuals reimbursed â€Å"under the table† might be capable of evading payment of the income taxes (Wisegeek.com). Conclusion Income tax is the main federal tax followed by the taxes on social insurance. The equality of federal tax is a significant issue in the system of the US taxation. The income tax is one of the major progressive constituents of the US system of tax and other types of taxes such as social insurance and sales taxes are normally regressive. Economicwatch.com. US Taxation, Taxation in United States, 2010. Web. Roach, Benard. â€Å"Progressive and Regressive Taxation in the United States: Who’s really paying (and not paying) their fair share?† 2003. Global Development E nvironment Institute, Working Paper No. 03-10. Unclefed.com. US Tax Treaties, 2006. Web. Wisegeek.com. What are the advantages and disadvantages of a tax on earnings? 2011. Web.

Friedrich Nietzsche's On The Genealogy of Morals Essay

Nietzsches Genealogy of Morality - Essay Example From this paper, it is clear that according to Nietzsche (57), morality no longer guides people but there are forced by different legal circumstances to behave in a given way. In this essay, the writer will try to evaluate and analyze the genealogy of morality as noted by Nietzsche (57). Understanding genealogy of morality is a great way for people to look back and gauge where they went wrong in reference to bad ethics and morals in the society. Nietzsche makes an assertion that one becomes forced to admit that legal conditions could be nothing other than means to create larger units of power (Nietzsche 57). He attacks the ideas that morality is selfless, the idea that suffering can be interpreted as rightful punishment to whoever experiences it because it sharpens their thinking on a given subject. He also argues on the conception of free will that involves the idea that agents could act differently from what they did (Nietzsche 57). Free will, even as anchored on the Holy Bible that God gave His people a free will to choose between what is right and wrong, is a big challenge to the society in reference to the decaying morals. The moral decay happens because people no longer adhere to any traditional customs that guide their ethics and morals because they are free to choose and behave any way they want despite societal values. He talks about a privileging of ‘slave values such as humility and devaluation of those such as pride and audacity, and the conception that morality involves obligations with unconditional obligations and that it is universally applicable or binding. Morality should be upheld at all instances, and governments should institute measures that will boost good morality for their citizens.

Poerty Essay Example | Topics and Well Written Essays - 500 words

Poerty - Essay Example Because each speaker conveys a personal narrative of love being the main subject, Donne and Blake necessitate to use elements that are naturally felt and are symbolic of certain human characteristics as reflected by the beauty and brilliance of the shining sun whereas the difference between clod and pebble serves to embody the opposing traits of sincerity and conceitedness. Blake’s three-part â€Å"The Clod and the Pebble† opens with â€Å"Love seeketh not itself to please, / Nor for itself hath any care† which is apparently stated by the â€Å"little Clod of Clay† in some rhythm. The clod is personified as one that sings about a selfless kind of love and knows what true love means for it has been innumerably stepped on in life. As the narrator further confesses the clod to have been â€Å"Trodden with the cattle’s feet†, the clod’s filth and humble situation explicates a virtuous character that is trained to deal with hardships so that the knowledge and deed of love becomes the essence of life. To imagine, the clay merely accepts man’s heavy toil and severe actions that are normally difficult to bear as it allows itself to be utilized as base to hold moving feet, dwellings, and transport of everyday. Thus, the clod proceeds with â€Å"But for another gives it ease, / And builds a heaven in hellà ¢â‚¬â„¢s despair† to signify how it sincerely means for love to function on someone else’s sake in generous terms. This is in huge contrast to the attitude of â€Å"Pebble of the brook† that claims â€Å"Love seeketh only Self to please, / To bind another to its delight† for in its evil selfishness, it sees and cares not about welfare of others whose loss would even matter in the fulfillment of self-love. On the other hand, Donne’s â€Å"The Sun Rising† communicates the meaning and significance of love through a speaker who seemingly dares the sun to put his spirit to test as he expresses â€Å"Love, all alike, no season knows nor clime†. As though the might of his love

My Life Learning Experience with R.S.V Essay Example for Free

My Life Learning Experience with R.S.V Essay R. S. V My Life Learning Experience with R. S. V Name Course Title Teacher Date Abstract Many individuals have experienced problems with their hospitals or health care facilities. An important concept that I learned from facing this family crisis that will be examined in this paper is that, when a family member becomes seriously ill, they need quality medical care. Sometimes, when a persons life is at stake, the further a person lives from medical facilities which can offer quality care can be a grave factor. R. S. V 1 R. S. V in Infants This paper will examine several lessons and concepts which I learned from personal life-learning experiences. Three examples that will be addressed in this paper will examine a different aspect of a certain life-learning experience. In researching and analyzing each aspect of a life-learning experience, this paper will examine the four elements of Kolbs Model of Experimental Learning. The first aspect of the lessons I learned after enduring a family crisis which this paper will explore includes how I learned about an illness that frequently affects infants called Respiratory Syncytial Virus. Respiratory Syncytial Virus, or RSV, is a respiratory virus which has many of the same symptoms as the common cold and is usually contracted by children during winter months. After my newborn son, Carter Forrest Barnhart began displaying symptoms of a common cold, my husband and I took Carter to his local pediatrician. Unfortunately, the pediatrician improperly diagnosed the virus as a simple common cold and sent Carter, my husband and I back home. However, after we returned home, his symptoms did not improve. Instead, he began coughing profusely and did not want to eat. I became greatly concerned about our sons health. Within a few days, Carter had lost weight and become weak. Then his breathing appeared to be abnormal, and my husband and I began to suspect that something else was wrong with Carter. R. S. V 2 By April 7th, 2002, Carters breathing problems got considerably worse, and my husband and I thought that he could possibly suffocate. So, in a desperate attempt to help Carters health, we brought our son to the nearest hospital. He was then hospital, arrangements needed to be made to send him to Charleston Area Medical Center. Carter later arrived safely at the Women and Childrens Hospital, a division of the Charleston Area Medical Center in Charleston, West Virginia. He was then placed in the hospitals Pediatric Intensive Care Unit, where he remained for five days. Looking back, I now realize the high importance of residing in communities which have high quality health care facilities. I learned that the first doctor who diagnosed my son did not diagnose Carter properly by failing to recognize that what looked like the common cold was actually Respiratory Syncytial Virus (RSV). The pediatricians error could have cost my son his life. After Carter was taken to the emergency room at our local hospital, I learned that, when someones life is at stake, the distance from a medical facility which can provide quality care is sometimes a life and death matter. Thus, one of the lessons that I learned by this life-learning experience is that it is important for all individuals to have quick access to a state of the art hospital or medical facility. A medical facility must be able to provide the excellent care that a seriously ill R. S. V 3 ndividual needs. In this example, a baby needed to be treated by a special infant care unit, which our local hospitals did not have. Therefore, the baby did not have ready access to the kind of medical facility that he needed. The proper medical facility can mean the difference of life or death, thus, I now understand that the quality of the medical facilities, and the services received from those facilities provided, is one of the important issues facing people today. Learning about the importance of living near a high quality health care facility helped me become amiliar with the idea that a person should be fully educated about the health services in his or her community before something critical occurs. I regretted the fact that we were not more prepared to deal with this crisis. Thus, I have since learned that I need to research the qualifications of any professional my child will be receiving treatment from. In the future, I will research hospitals or schools before enrolling my child in them. I can also apply the concept that quality care is an important aspect of a persons life to other situations as well. For example, I will have o make sure that my child has a qualified pediatrician and dentist to take care of his health needs in the future. I will also have to ensure that my child gets his vaccinations. Moreover, I learned that there is no substitute for being prepared for an emergency situation. I plan on researching the response time of our police and fire departments and plan to learn about the efficiency of our ambulance services. Another part of the lessons I learned while confronting this family crisis is how I learned that high quality heath care is best provided by highly qualified doctors. I lso learned that an unqualified doctor may easily misdiagnose a patients symptoms. The discussion below will show how I have learned to ask questions before selecting a pediatrician. My son was initially treated by a pediatrician who misdiagnosed the babys medical symptoms and declared that our infant was we were told to take our child home and give him some cold medicine. This was our childs only treatment, and the medicine did not work. Carters symptoms did not improve after a reasonable period of time. Thus, my husband and I began to suspect that something else could be wrong. Then, when our baby turned pasty in color, started to cry inconsolably, refused to eat or drink anything, lost weight, and then hardly cried or moved in his crib, my husband and I became more concerned. We later learned that Carter had RSV and double pneumonia. Since then, I have spoken to many doctors about rural medicine. One of the doctors I spoke to that works at our local hospital explained in a recent personal interview which I conducted with him that many people do not ask enough questions of their doctors after they have been told the results of a diagnosis. He advised that potential atients should ask about all terms that describe the problem and that the doctor should fully explain the R. S. V 5 condition to the patient. More importantly, when the patient is a baby, the infants parents need to understand the complete diagnosis of their childs condition The doctor also said that a great deal of rural patients do not know how to properly ask their doctors specific questions related to the diagnosis. Therefore, rural doctors need to take more time to explain things to their patients, especially in cases where doctors are not absolutely sure of the diagnosis. I was also told that some patients have no reason to be told when something is misdiagnosed as nothing more than the common cold, especially when a childs doctor confidently tells an infants parents that the symptoms should improve when the baby took the cold medicine. The lesson is that parents must be very careful when choosing a pediatrician. I learned that a good pediatrician knows how to check a baby for a variety of diseases. In the case of my son, the first pediatrician failed to properly diagnose the baby because he was, at the very least, was not familiar with the symptoms of RSV. Thus, I learned that receiving treatment from a qualified pediatrician is an essential part of a childs health care. I also realized, in other areas of my life, I need to be certain that I am qualified to perform any Job that I might later want to undertake. So it is imperative that I take my education as serious as possible so that I will later be prepared to succeed in my chosen career. R. S. V6 Another important concept that I learned through my life-learning experience is that Just like other people, doctors make errors too. Unfortunately, a doctors mistake can cause the loss of ones life. Any professional should avoid making unnecessary mistakes at all times. Therefore, I would like to avoid making mistakes which would be considered negligence in my chosen career. Thus, I now believe that I need as much training in the field of health care management as possible, because that is the field which I intend to begin my professional career once I have received my Bachelors Degree. I also now would like to become actively involved in professional organizations and associations in which school friends and successful will help me exchange information with other health care management professionals hich will hopefully help me keep atop of current developments in my field. The third aspect of the lessons I learned which this paper will explore is that many rural health care facilities in America do not have up to date equipment. I also learned that, for the past several years, many local family health care facilities have suffered from recent cutbacks in federal grant money. This paper will now discuss my findings about the importance of selecting a health care facility which has up to date equipment and employees that keep on top of current developments in the medical ield. R. S. V7 Not only were the doctors more knowledgeable at the Women and Childrens Hospital in Charleston, but the doctors at the hospital in Charleston also had more current equipment and also performed their duties much more quickly and efficiently than the doctors at the local hospital. I learned that, when the life of a loved one is at stake, a hospital with modern equipment and trained staff can mean the difference between life and death. I also now believe that parents should visit the local hospitals before their first child is ever born to make sure those hospitals re not understaffed, dirty, or not funded properly. While larger hospitals may charge more money for visits, the money paid for a proper diagnosis at a quality facility is far less than the money one might pay if an illness is misdiagnosed. In addition, local medical care facilities need to provide quality, up to date services to their patients. In this situation, Carter needed to be treated in a special care unit in which patients are attached to electronic monitors which track vital functions as well as to other equipment that support breathing (Roberts, 1993, p. 170). Unfortunately, only larger acilities usually have modern pediatric intensive care units, and large hospitals are not all cities. I have learned that a high quality health care facility should have up to date equipment. Modern equipment is essential to provide patients with the best possible R. S. V8 health care. However, a lot of rural hospitals cannot afford this. The issue of a facility which does not have modern equipment is a very important one, and the concept applies to other situations which I may have to deal with later on. For instance, I will want to make sure that, any school my child is enrolled in should have adequate acilities. I will want to ensure that the school has smoke detectors in every classroom and that the fire extinguishers are in proper working order. This paper analyzed the various lessons and concepts that I learned from some life-learning experiences. Each of the papers three parts explored a different aspect of my experiences. This paper used the four elements of Kolbs Model of Experimental Learning to detail how I used the lessons during a family crisis. R. S. V9 References Mesa, CA: ICN Pharmaceuticals. Roberts, M. J. (1993). Your Money or Your Life: The Health Care Crisis Explained. New York: Doubleday.

The Multiple Organ Dysfunction Syndrome Essays -- traumatic, neurogenic

There is a variety of different types of shock and each type can be caused by many different things. â€Å"Shock is classified as cardiogenic (caused by heart failure); neurogenic or vasogenic (caused by alterations in vascular smooth muscle tone); anaphylactic (caused by hypersensitivity); septic (caused by infection); or hypovolemic (caused by insufficient intravascular fluid volume)† (Huether, McCance, 2010, pp.1696-1697). There is also traumatic shock which is similar to hypovolemic shock and septic shock. Each case of shock is important and needs to be monitored carefully. One type of shock to consider is neurogenic shock. Neurogenic shock is often referred to as vasogenic shock. This type of shock generally occurs from an imbalance of stimulation of vascular smooth muscle. â€Å"Neurogenic shock can be caused by any factor that stimulates parasympathetic activity or inhibits sympathetic activity of vascular smooth muscle† (Huether, McCance, 2010, pp. 1702). One of the factors that can cause neurogenic shock is trauma to the spinal cord. For example, a man named John Jackson suffered a spinal cord injury after being involved in a motorcycle accident; he will likely suffer from neurogenic shock as well. While he is in neurogenic shock however, he has not lost any fluid from vasculature. This is possible because when the spinal cord is injured there can also be injury to the nerve that controls the blood vessels width (Shock, 2013). This leads to a drop in blood pressure because the blood vessels relax and expand, thus leading to a lack of loss of fluid from vasculature. Even though the individu al is in neurogenic shock, the type of injury that is causing the shock can alter what the patient is experiencing. A patient that has a diff... ...6, January). From Inflammation to MODS: Stopping Sepsis in its Tracks. In Lippincott's Nursing Center. Retrieved December 11, 2013, from http://www.nursingcenter.com/lnc/static?pageid=733523 Huether, S. E., & McCance, K. L. (2010). Pathophysiology- The Biologic Basis for Disease in Adults and Children (sixth ed., pp. 1696-1727). Maryland Heights, MO: Mosby Elsevier. Marshall, J. C. (2001). The Multiple Organ Dysfunction Syndrome. In NCBI. Retrieved December 11, 2013, from http://www.ncbi.nlm.nih.gov/books/NBK6868/ Sheridan, R. L. (2013, June 10). Initial Evaluation and Management of the Burn Patient. In Medscape. Retrieved December 11, 2013, from http://emedicine.medscape.com/article/435402-overview#showall Shock. (2013, February). In Better Health Channel. Retrieved December 11, 2013, from http://www.betterhealth.vic.gov.au/bhcv2/bhcarticles.nsf/pages/Shock

Mlc Cheat Sheet

mkThis page intentionally left blank Actuarial Mathematics for Life Contingent Risks How can actuaries best equip themselves for the products and risk structures of the future? In this new textbook, three leaders in actuarial science give a modern perspective on life contingencies. The book begins traditionally, covering actuarial models and theory, and emphasizing practical applications using computational techniques. The authors then develop a more contemporary outlook, introducing multiple state models, emerging cash ? ws and embedded options. Using spreadsheet-style software, the book presents large-scale, realistic examples. Over 150 exercises and solutions teach skills in simulation and projection through computational practice. Balancing rigour with intuition, and emphasizing applications, this textbook is ideal not only for university courses, but also for individuals preparing for professional actuarial examinations and quali? ed actuaries wishing to renew and update their skills.International Series on Actuarial Science Christopher Daykin, Independent Consultant and Actuary Angus Macdonald, Heriot-Watt University The International Series on Actuarial Science, published by Cambridge University Press in conjunction with the Institute of Actuaries and the Faculty of Actuaries, contains textbooks for students taking courses in or related to actuarial science, as well as more advanced works designed for continuing professional development or for describing and synthesizing research.The series is a vehicle for publishing books that re? ect changes and developments in the curriculum, that encourage the introduction of courses on actuarial science in universities, and that show how actuarial science can be used in all areas where there is long-term ? nancial risk. ACTUARIAL MATHEMATICS FOR LIFE CONTINGENT RISKS D AV I D C . M . D I C K S O N University of Melbourne M A RY R . H A R D Y University of Waterloo, Ontario H O WA R D R . WAT E R S Heriot-Watt Univ ersity, Edinburgh CAMBRIDGE UNIVERSITY PRESSCambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo, Delhi, Dubai, Tokyo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www. cambridge. org Information on this title: www. cambridge. org/9780521118255  © D. C. M. Dickson, M. R. Hardy and H. R. Waters 2009 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.First published in print format 2009 ISBN-13 ISBN-13 978-0-511-65169-4 978-0-521-11825-5 eBook (NetLibrary) Hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. To Carolann, Vivien and Phelim Contents Preface page xiv 1 Introduction to life insurance 1 1. 1 Summary 1 1. 2 Background 1 1. 3 Life insurance and annuity contracts 3 1. 3. 1 Introduction 3 1. 3. Traditional insurance contracts 4 1. 3. 3 Modern insurance contracts 6 1. 3. 4 Distribution methods 8 1. 3. 5 Underwriting 8 1. 3. 6 Premiums 10 1. 3. 7 Life annuities 11 1. 4 Other insurance contracts 12 1. 5 Pension bene? ts 12 1. 5. 1 De? ned bene? t and de? ned contribution pensions 13 1. 5. 2 De? ned bene? t pension design 13 1. 6 Mutual and proprietary insurers 14 1. 7 Typical problems 14 1. 8 Notes and further reading 15 1. 9 Exercises 15 2 Survival models 17 2. 1 Summary 17 2. 2 The future lifetime random variable 17 2. 3 The force of mortality 21 2. 4 Actuarial notation 26 2. Mean and standard deviation of Tx 29 2. 6 Curtate future lifetime 32 2. 6. 1 Kx and ex 32 vii viii 2. 6. 2 Contents The complete and curtate expected fu ture ? lifetimes, ex and ex 2. 7 Notes and further reading 2. 8 Exercises Life tables and selection 3. 1 Summary 3. 2 Life tables 3. 3 Fractional age assumptions 3. 3. 1 Uniform distribution of deaths 3. 3. 2 Constant force of mortality 3. 4 National life tables 3. 5 Survival models for life insurance policyholders 3. 6 Life insurance underwriting 3. 7 Select and ultimate survival models 3. 8 Notation and formulae for select survival models 3. Select life tables 3. 10 Notes and further reading 3. 11 Exercises Insurance bene? ts 4. 1 Summary 4. 2 Introduction 4. 3 Assumptions 4. 4 Valuation of insurance bene? ts ? 4. 4. 1 Whole life insurance: the continuous case, Ax 4. 4. 2 Whole life insurance: the annual case, Ax (m) 4. 4. 3 Whole life insurance: the 1/mthly case, Ax 4. 4. 4 Recursions 4. 4. 5 Term insurance 4. 4. 6 Pure endowment 4. 4. 7 Endowment insurance 4. 4. 8 Deferred insurance bene? ts (m) ? 4. 5 Relating Ax , Ax and Ax 4. 5. 1 Using the uniform distribution of deaths assu mption 4. 5. 2 Using the claims acceleration approach 4. Variable insurance bene? ts 4. 7 Functions for select lives 4. 8 Notes and further reading 4. 9 Exercises Annuities 5. 1 Summary 5. 2 Introduction 3 4 34 35 36 41 41 41 44 44 48 49 52 54 56 58 59 67 67 73 73 73 74 75 75 78 79 81 86 88 89 91 93 93 95 96 101 101 102 107 107 107 5 Contents 5. 3 5. 4 Review of annuities-certain Annual life annuities 5. 4. 1 Whole life annuity-due 5. 4. 2 Term annuity-due 5. 4. 3 Whole life immediate annuity 5. 4. 4 Term immediate annuity 5. 5 Annuities payable continuously 5. 5. 1 Whole life continuous annuity 5. 5. 2 Term continuous annuity 5. 6 Annuities payable m times per year 5. . 1 Introduction 5. 6. 2 Life annuities payable m times a year 5. 6. 3 Term annuities payable m times a year 5. 7 Comparison of annuities by payment frequency 5. 8 Deferred annuities 5. 9 Guaranteed annuities 5. 10 Increasing annuities 5. 10. 1 Arithmetically increasing annuities 5. 10. 2 Geometrically increasing annu ities 5. 11 Evaluating annuity functions 5. 11. 1 Recursions 5. 11. 2 Applying the UDD assumption 5. 11. 3 Woolhouse’s formula 5. 12 Numerical illustrations 5. 13 Functions for select lives 5. 14 Notes and further reading 5. 15 Exercises Premium calculation 6. 1 Summary 6. 2 Preliminaries 6. Assumptions 6. 4 The present value of future loss random variable 6. 5 The equivalence principle 6. 5. 1 Net premiums 6. 6 Gross premium calculation 6. 7 Pro? t 6. 8 The portfolio percentile premium principle 6. 9 Extra risks 6. 9. 1 Age rating 6. 9. 2 Constant addition to  µx 6. 9. 3 Constant multiple of mortality rates ix 108 108 109 112 113 114 115 115 117 118 118 119 120 121 123 125 127 127 129 130 130 131 132 135 136 137 137 142 142 142 143 145 146 146 150 154 162 165 165 165 167 6 x Contents 6. 10 Notes and further reading 6. 11 Exercises Policy values 7. 1 Summary 7. 2 Assumptions 7. Policies with annual cash ? ows 7. 3. 1 The future loss random variable 7. 3. 2 Policy values for policies with annual cash ? ows 7. 3. 3 Recursive formulae for policy values 7. 3. 4 Annual pro? t 7. 3. 5 Asset shares 7. 4 Policy values for policies with cash ? ows at discrete intervals other than annually 7. 4. 1 Recursions 7. 4. 2 Valuation between premium dates 7. 5 Policy values with continuous cash ? ows 7. 5. 1 Thiele’s differential equation 7. 5. 2 Numerical solution of Thiele’s differential equation 7. 6 Policy alterations 7. 7 Retrospective policy value 7. 8 Negative policy values 7. Notes and further reading 7. 10 Exercises Multiple state models 8. 1 Summary 8. 2 Examples of multiple state models 8. 2. 1 The alive–dead model 8. 2. 2 Term insurance with increased bene? t on accidental death 8. 2. 3 The permanent disability model 8. 2. 4 The disability income insurance model 8. 2. 5 The joint life and last survivor model 8. 3 Assumptions and notation 8. 4 Formulae for probabilities 8. 4. 1 Kolmogorov’s forward equations 8. 5 Numerical evaluat ion of probabilities 8. 6 Premiums 8. 7 Policy values and Thiele’s differential equation 8. 7. 1 The disability income model 8. 7. Thiele’s differential equation – the general case 169 170 176 176 176 176 176 182 191 196 200 203 204 205 207 207 211 213 219 220 220 220 230 230 230 230 232 232 233 234 235 239 242 243 247 250 251 255 7 8 Contents 8. 8 8. 9 Multiple decrement models Joint life and last survivor bene? ts 8. 9. 1 The model and assumptions 8. 9. 2 Joint life and last survivor probabilities 8. 9. 3 Joint life and last survivor annuity and insurance functions 8. 9. 4 An important special case: independent survival models 8. 10 Transitions at speci? ed ages 8. 11 Notes and further reading 8. 12 Exercises Pension mathematics 9. Summary 9. 2 Introduction 9. 3 The salary scale function 9. 4 Setting the DC contribution 9. 5 The service table 9. 6 Valuation of bene? ts 9. 6. 1 Final salary plans 9. 6. 2 Career average earnings plans 9. 7 Funding plans 9. 8 Not es and further reading 9. 9 Exercises Interest rate risk 10. 1 Summary 10. 2 The yield curve 10. 3 Valuation of insurances and life annuities 10. 3. 1 Replicating the cash ? ows of a traditional non-participating product 10. 4 Diversi? able and non-diversi? able risk 10. 4. 1 Diversi? able mortality risk 10. 4. 2 Non-diversi? able risk 10. 5 Monte Carlo simulation 10. Notes and further reading 10. 7 Exercises Emerging costs for traditional life insurance 11. 1 Summary 11. 2 Pro? t testing for traditional life insurance 11. 2. 1 The net cash ? ows for a policy 11. 2. 2 Reserves 11. 3 Pro? t measures 11. 4 A further example of a pro? t test xi 256 261 261 262 264 270 274 278 279 290 290 290 291 294 297 306 306 312 314 319 319 326 326 326 330 332 334 335 336 342 348 348 353 353 353 353 355 358 360 9 10 11 xii Contents 11. 5 Notes and further reading 11. 6 Exercises Emerging costs for equity-linked insurance 12. 1 Summary 12. 2 Equity-linked insurance 12. 3 Deterministic pro? testing fo r equity-linked insurance 12. 4 Stochastic pro? t testing 12. 5 Stochastic pricing 12. 6 Stochastic reserving 12. 6. 1 Reserving for policies with non-diversi? able risk 12. 6. 2 Quantile reserving 12. 6. 3 CTE reserving 12. 6. 4 Comments on reserving 12. 7 Notes and further reading 12. 8 Exercises Option pricing 13. 1 Summary 13. 2 Introduction 13. 3 The ‘no arbitrage’ assumption 13. 4 Options 13. 5 The binomial option pricing model 13. 5. 1 Assumptions 13. 5. 2 Pricing over a single time period 13. 5. 3 Pricing over two time periods 13. 5. 4 Summary of the binomial model option pricing technique 13. The Black–Scholes–Merton model 13. 6. 1 The model 13. 6. 2 The Black–Scholes–Merton option pricing formula 13. 7 Notes and further reading 13. 8 Exercises Embedded options 14. 1 Summary 14. 2 Introduction 14. 3 Guaranteed minimum maturity bene? t 14. 3. 1 Pricing 14. 3. 2 Reserving 14. 4 Guaranteed minimum death bene? t 14. 4. 1 Pricing 14. 4. 2 Reserving 369 369 374 374 374 375 384 388 390 390 391 393 394 395 395 401 401 401 402 403 405 405 405 410 413 414 414 416 427 428 431 431 431 433 433 436 438 438 440 12 13 14 Contents 14. 5 Pricing methods for embedded options 14. 6 Risk management 14. 7 Emerging costs 14. Notes and further reading 14. 9 Exercises A Probability theory A. 1 Probability distributions A. 1. 1 Binomial distribution A. 1. 2 Uniform distribution A. 1. 3 Normal distribution A. 1. 4 Lognormal distribution A. 2 The central limit theorem A. 3 Functions of a random variable A. 3. 1 Discrete random variables A. 3. 2 Continuous random variables A. 3. 3 Mixed random variables A. 4 Conditional expectation and conditional variance A. 5 Notes and further reading B Numerical techniques B. 1 Numerical integration B. 1. 1 The trapezium rule B. 1. 2 Repeated Simpson’s rule B. 1. 3 Integrals over an in? nite interval B. Woolhouse’s formula B. 3 Notes and further reading C Simulation C. 1 The inverse transf orm method C. 2 Simulation from a normal distribution C. 2. 1 The Box–Muller method C. 2. 2 The polar method C. 3 Notes and further reading References Author index Index xiii 444 447 449 457 458 464 464 464 464 465 466 469 469 470 470 471 472 473 474 474 474 476 477 478 479 480 480 481 482 482 482 483 487 488 Preface Life insurance has undergone enormous change in the last two to three decades. New and innovative products have been developed at the same time as we have seen vast increases in computational power.In addition, the ? eld of ? nance has experienced a revolution in the development of a mathematical theory of options and ? nancial guarantees, ? rst pioneered in the work of Black, Scholes and Merton, and actuaries have come to realize the importance of that work to risk management in actuarial contexts. Given the changes occurring in the interconnected worlds of ? nance and life insurance, we believe that this is a good time to recast the mathematics of life continge nt risk to be better adapted to the products, science and technology that are relevant to current and future actuaries.In this book we have developed the theory to measure and manage risks that are contingent on demographic experience as well as on ? nancial variables. The material is presented with a certain level of mathematical rigour; we intend for readers to understand the principles involved, rather than to memorize methods or formulae. The reason is that a rigorous approach will prove more useful in the long run than a short-term utilitarian outlook, as theory can be adapted to changing products and technology in ways that techniques, without scienti? c support, cannot.We start from a traditional approach, and then develop a more contemporary perspective. The ? rst seven chapters set the context for the material, and cover traditional actuarial models and theory of life contingencies, with modern computational techniques integrated throughout, and with an emphasis on the prac tical context for the survival models and valuation methods presented. Through the focus on realistic contracts and assumptions, we aim to foster a general business awareness in the life insurance context, at the same time as we develop the mathematical tools for risk management in that context. iv Preface xv In Chapter 8 we introduce multiple state models, which generalize the life– death contingency structure of previous chapters. Using multiple state models allows a single framework for a wide range of insurance, including bene? ts which depend on health status, on cause of death bene? ts, or on two or more lives. In Chapter 9 we apply the theory developed in the earlier chapters to problems involving pension bene? ts. Pension mathematics has some specialized concepts, particularly in funding principles, but in general this chapter is an application of the theory in the preceding chapters.In Chapter 10 we move to a more sophisticated view of interest rate models and intere st rate risk. In this chapter we explore the crucially important difference between diversi? able and non-diversi? able risk. Investment risk represents a source of non-diversi? able risk, and in this chapter we show how we can reduce the risk by matching cash ? ows from assets and liabilities. In Chapter 11 we continue the cash ? ow approach, developing the emerging cash ? ows for traditional insurance products. One of the liberating aspects of the computer revolution for actuaries is that we are no longer required to summarize complex bene? s in a single actuarial value; we can go much further in projecting the cash ? ows to see how and when surplus will emerge. This is much richer information that the actuary can use to assess pro? tability and to better manage portfolio assets and liabilities. In Chapter 12 we repeat the emerging cash ? ow approach, but here we look at equity-linked contracts, where a ? nancial guarantee is commonly part of the contingent bene? t. The real risks for such products can only be assessed taking the random variation in potential outcomes into consideration, and we demonstrate this with Monte Carlo simulation of the emerging cash ? ws. The products that are explored in Chapter 12 contain ? nancial guarantees embedded in the life contingent bene? ts. Option theory is the mathematics of valuation and risk management of ? nancial guarantees. In Chapter 13 we introduce the fundamental assumptions and results of option theory. In Chapter 14 we apply option theory to the embedded options of ? nancial guarantees in insurance products. The theory can be used for pricing and for determining appropriate reserves, as well as for assessing pro? tability.The material in this book is designed for undergraduate and graduate programmes in actuarial science, and for those self-studying for professional actuarial exams. Students should have suf? cient background in probability to be able to calculate moments of functions of one or two random vari ables, and to handle conditional expectations and variances. We also assume familiarity with the binomial, uniform, exponential, normal and lognormal distributions. Some of the more important results are reviewed in Appendix A. We also assume xvi Preface that readers have completed an introductory level course in the mathematics of ? ance, and are aware of the actuarial notation for annuities-certain. Throughout, we have opted to use examples that liberally call on spreadsheetstyle software. Spreadsheets are ubiquitous tools in actuarial practice, and it is natural to use them throughout, allowing us to use more realistic examples, rather than having to simplify for the sake of mathematical tractability. Other software could be used equally effectively, but spreadsheets represent a fairly universal language that is easily accessible. To keep the computation requirements reasonable, we have ensured hat every example and exercise can be completed in Microsoft Excel, without needing an y VBA code or macros. Readers who have suf? cient familiarity to write their own code may ? nd more ef? cient solutions than those that we have presented, but our principle was that no reader should need to know more than the basic Excel functions and applications. It will be very useful for anyone working through the material of this book to construct their own spreadsheet tables as they work through the ? rst seven chapters, to generate mortality and actuarial functions for a range of mortality models and interest rates.In the worked examples in the text, we have worked with greater accuracy than we record, so there will be some differences from rounding when working with intermediate ? gures. One of the advantages of spreadsheets is the ease of implementation of numerical integration algorithms. We assume that students are aware of the principles of numerical integration, and we give some of the most useful algorithms in Appendix B. The material in this book is appropriate for tw o one-semester courses. The ? rst seven chapters form a fairly traditional basis, and would reasonably constitute a ? st course. Chapters 8–14 introduce more contemporary material. Chapter 13 may be omitted by readers who have studied an introductory course covering pricing and delta hedging in a Black–Scholes–Merton model. Chapter 9, on pension mathematics, is not required for subsequent chapters, and could be omitted if a single focus on life insurance is preferred. Acknowledgements Many of our students and colleagues have made valuable comments on earlier drafts of parts of the book. Particular thanks go to Carole Bernard, Phelim Boyle, Johnny Li, Ana Maria Mera, Kok Keng Siaw and Matthew Till.The authors gratefully acknowledge the contribution of the Departments of Statistics and Actuarial Science, University of Waterloo, and Actuarial Mathematics and Statistics, Heriot-Watt University, in welcoming the non-resident Preface xvii authors for short visits to w ork on this book. These visits signi? cantly shortened the time it has taken to write the book (to only one year beyond the original deadline). David Dickson University of Melbourne Mary Hardy University of Waterloo Howard Waters Heriot-Watt University 1 Introduction to life insurance 1. Summary Actuaries apply scienti? c principles and techniques from a range of other disciplines to problems involving risk, uncertainty and ? nance. In this chapter we set the context for the mathematics of later chapters, by describing some of the background to modern actuarial practice in life insurance, followed by a brief description of the major types of life insurance products that are sold in developed insurance markets. Because pension liabilities are similar in many ways to life insurance liabilities, we also describe some common pension bene? ts.We give examples of the actuarial questions arising from the risk management of these contracts. How to answer such questions, and solve the result ing problems, is the subject of the following chapters. 1. 2 Background The ? rst actuaries were employed by life insurance companies in the early eighteenth century to provide a scienti? c basis for managing the companies’ assets and liabilities. The liabilities depended on the number of deaths occurring amongst the insured lives each year. The modelling of mortality became a topic of both commercial and general scienti? interest, and it attracted many signi? cant scientists and mathematicians to actuarial problems, with the result that much of the early work in the ? eld of probability was closely connected with the development of solutions to actuarial problems. The earliest life insurance policies provided that the policyholder would pay an amount, called the premium, to the insurer. If the named life insured died during the year that the contract was in force, the insurer would pay a predetermined lump sum, the sum insured, to the policyholder or his or her estate. So, t he ? st life insurance contracts were annual contracts. Each year the premium would increase as the probability of death increased. If the insured life became very ill at the renewal date, the insurance might not be renewed, in which case 1 2 Introduction to life insurance no bene? t would be paid on the life’s subsequent death. Over a large number of contracts, the premium income each year should approximately match the claims outgo. This method of matching income and outgo annually, with no attempt to smooth or balance the premiums over the years, is called assessmentism.This method is still used for group life insurance, where an employer purchases life insurance cover for its employees on a year-to-year basis. The radical development in the later eighteenth century was the level premium contract. The problem with assessmentism was that the annual increases in premiums discouraged policyholders from renewing their contracts. The level premium policy offered the policyholde r the option to lock-in a regular premium, payable perhaps weekly, monthly, quarterly or annually, for a number of years.This was much more popular with policyholders, as they would not be priced out of the insurance contract just when it might be most needed. For the insurer, the attraction of the longer contract was a greater likelihood of the policyholder paying premiums for a longer period. However, a problem for the insurer was that the longer contracts were more complex to model, and offered more ? nancial risk. For these contracts then, actuarial techniques had to develop beyond the year-to-year modelling of mortality probabilities. In particular, it became necessary to incorporate ? nancial considerations into the modelling of income and outgo.Over a one-year contract, the time value of money is not a critical aspect. Over, say, a 30-year contract, it becomes a very important part of the modelling and management of risk. Another development in life insurance in the nineteent h century was the concept of insurable interest. This was a requirement in law that the person contracting to pay the life insurance premiums should face a ? nancial loss on the death of the insured life that was no less than the sum insured under the policy. The insurable interest requirement disallowed the use of insurance as a form of gambling on the lives of public ? ures, but more importantly, removed the incentive for a policyholder to hasten the death of the named insured life. Subsequently, insurance policies tended to be purchased by the insured life, and in the rest of this book we use the convention that the policyholder who pays the premiums is also the life insured, whose survival or death triggers the payment of the sum insured under the conditions of the contract. The earliest studies of mortality include life tables constructed by John Graunt and Edmund Halley. A life table summarizes a survival model by specifying the proportion of lives that are expected to survive to each age.Using London mortality data from the early seventeenth century, Graunt proposed, for example, that each new life had a probability of 40% of surviving to age 16, and a probability of 1% of surviving to age 76. Edmund Halley, famous for his astronomical calculations, used mortality data from the city of Breslau in the late seventeenth century as the basis for his life table, which, like Graunt’s, was constructed by 1. 3 Life insurance and annuity contracts 3 proposing the average (‘medium’ in Halley’s phrase) proportion of survivors to each age from an arbitrary number of births.Halley took the work two steps further. First, he used the table to draw inference about the conditional survival probabilities at intermediate ages. That is, given the probability that a newborn life survives to each subsequent age, it is possible to infer the probability that a life aged, say, 20, will survive to each subsequent age, using the condition that a life ag ed zero survives to age 20. The second major innovation was that Halley combined the mortality data with an assumption about interest rates to ? nd the value of a whole life annuity at different ages.A whole life annuity is a contract paying a level sum at regular intervals while the named life (the annuitant) is still alive. The calculations in Halley’s paper bear a remarkable similarity to some of the work still used by actuaries in pensions and life insurance. This book continues in the tradition of combining models of mortality with models in ? nance to develop a framework for pricing and risk management of long-term policies in life insurance. Many of the same techniques are relevant also in pensions mathematics. However, there have been many changes since the ? st long-term policies of the late eighteenth century. 1. 3 Life insurance and annuity contracts 1. 3. 1 Introduction The life insurance and annuity contracts that were the object of study of the early actuaries w ere very similar to the contracts written up to the 1980s in all the developed insurance markets. Recently, however, the design of life insurance products has radically changed, and the techniques needed to manage these more modern contracts are more complex than ever. The reasons for the changes include: †¢ Increased interest by the insurers in offering combined savings and insurance †¢ †¢ †¢ products. The original life insurance products offered a payment to indemnify (or offset) the hardship caused by the death of the policyholder. Many modern contracts combine the indemnity concept with an opportunity to invest. More powerful computational facilities allow more complex products to be modelled. Policyholders have become more sophisticated investors, and require more options in their contracts, allowing them to vary premiums or sums insured, for example. More competition has led to insurers creating increasingly complex products in order to attract more busines s.The risk management techniques in ? nancial products have also become increasingly complex, and insurers have offered some bene? ts, particularly 4 Introduction to life insurance ? nancial guarantees, that require sophisticated techniques from ? nancial engineering to measure and manage the risk. In the remainder of this section we describe some of the most important modern insurance contracts, which will later be used as examples in the book. Different countries have different names and types of contracts; we have tried to cover the major contract types in North America, the United Kingdom and Australia.The basic transaction of life insurance is an exchange; the policyholder pays premiums in return for a later payment from the insurer which is life contingent, by which we mean that it depends on the death or survival or possibly the state of health of the policyholder. We usually use the term ‘insurance’ when the bene? t is paid as a single lump sum, either on the de ath of the policyholder or on survival to a predetermined maturity date. (In the UK it is common to use the term ‘assurance’ for insurance contracts involving lives, and insurance for contracts involving property. ) An annuity is a bene? in the form of a regular series of payments, usually conditional on the survival of the policyholder. 1. 3. 2 Traditional insurance contracts Term, whole life and endowment insurance are the traditional products, providing cash bene? ts on death or maturity, usually with predetermined premium and bene? t amounts. We describe each in a little more detail here. Term insurance pays a lump sum bene? t on the death of the policyholder, provided death occurs before the end of a speci? ed term. Term insurance allows a policyholder to provide a ? xed sum for his or her dependents in the event of the policyholder’s death.Level term insurance indicates a level sum insured and regular, level premiums. Decreasing term insurance indicates tha t the sum insured and (usually) premiums decrease over the term of the contract. Decreasing term insurance is popular in the UK where it is used in conjunction with a home mortgage; if the policyholder dies, the remaining mortgage is paid from the term insurance proceeds. Renewable term insurance offers the policyholder the option of renewing the policy at the end of the original term, without further evidence of the policyholder’s health status.In North America, Yearly Renewable Term (YRT) insurance is common, under which insurability is guaranteed for some ? xed period, though the contract is written only for one year at a time. 1. 3 Life insurance and annuity contracts 5 Convertible term insurance offers the policyholder the option to convert to a whole life or endowment insurance at the end of the original term, without further evidence of the policyholder’s health status. Whole life insurance pays a lump sum bene? t on the death of the policyholder whenever it occ urs.For regular premium contracts, the premium is often payable only up to some maximum age, such as 80. This avoids the problem that older lives may be less able to pay the premiums. Endowment insurance offers a lump sum bene? t paid either on the death of the policyholder or at the end of a speci? ed term, whichever occurs ? rst. This is a mixture of a term insurance bene? t and a savings element. If the policyholder dies, the sum insured is paid just as under term insurance; if the policyholder survives, the sum insured is treated as a maturing investment. Endowment insurance is obsolete in many jurisdictions.Traditional endowment insurance policies are not currently sold in the UK, but there are large portfolios of policies on the books of UK insurers, because until the late 1990s, endowment insurance policies were often used to repay home mortgages. The policyholder (who is the home owner) paid interest on the mortgage loan, and the principal was paid from the proceeds on the e ndowment insurance, either on the death of the policyholder or at the ? nal mortgage repayment date. Endowment insurance policies are becoming popular in developing nations, particularly for ‘micro-insurance’ where the amounts involved are small.It is hard for small investors to achieve good rates of return on investments, because of heavy expense charges. By pooling the death and survival bene? ts under the endowment contract, the policyholder gains on the investment side from the resulting economies of scale, and from the investment expertise of the insurer. With-pro? t insurance Also part of the traditional design of insurance is the division of business into ‘with-pro? t’ (also known, especially in North America, as ‘participating’, or ‘par’ business), and ‘without pro? t’ (also known as ‘non-participating’ or ‘non-par’). Under with-pro? t arrangements, the pro? s earned on the invested pr emiums are shared with the policyholders. In North America, the with-pro? t arrangement often takes the form of cash dividends or reduced premiums. In the UK and in Australia the traditional approach is to use the pro? ts to increase the sum insured, through bonuses called ‘reversionary bonuses’and ‘terminal bonuses’. Reversionary bonuses are awarded during the term of the contract; once a reversionary bonus is awarded it is guaranteed. Terminal bonuses are awarded when the policy matures, either through the death of the insured, or when an endowment policy reaches the end of the term.Reversionary bonuses 6 Introduction to life insurance Table 1. 1. Year 1 2 3 . . . Bonus on original sum insured 2% 2. 5% 2. 5% . . . Bonus on bonus 5% 6% 6% . . . Total bonus 2000. 00 4620. 00 7397. 20 . . . may be expressed as a percentage of the total of the previous sum insured plus bonus, or as a percentage of the original sum insured plus a different percentage of the pr eviously declared bonuses. Reversionary and terminal bonuses are determined by the insurer based on the investment performance of the invested premiums. For example, suppose an insurance is issued with sum insured $100 000.At the end of the ? rst year of the contract a bonus of 2% on the sum insured and 5% on previous bonuses is declared; in the following two years, the rates are 2. 5% and 6%. Then the total guaranteed sum insured increases each year as shown in Table 1. 1. If the policyholder dies, the total death bene? t payable would be the original sum insured plus reversionary bonuses already declared, increased by a terminal bonus if the investment returns earned on the premiums have been suf? cient. With-pro? ts contracts may be used to offer policyholders a savings element with their life insurance.However, the traditional with-pro? t contract is designed primarily for the life insurance cover, with the savings aspect a secondary feature. 1. 3. 3 Modern insurance contracts I n recent years insurers have provided more ? exible products that combine the death bene? t coverage with a signi? cant investment element, as a way of competing for policyholders’savings with other institutions, for example, banks or open-ended investment companies (e. g. mutual funds in North America, or unit trusts in the UK). Additional ?exibility also allows policyholders to purchase less insurance when their ? ances are tight, and then increase the insurance coverage when they have more money available. In this section we describe some examples of modern, ? exible insurance contracts. Universal life insurance combines investment and life insurance. The policyholder determines a premium and a level of life insurance cover. Some 1. 3 Life insurance and annuity contracts 7 of the premium is used to fund the life insurance; the remainder is paid into an investment fund. Premiums are ? exible, as long as they are suf? cient to pay for the designated sum insured under the ter m insurance part of the contract.Under variable universal life, there is a range of funds available for the policyholder to select from. Universal life is a common insurance contract in North America. Unitized with-pro? t is a UK insurance contract; it is an evolution from the conventional with-pro? t policy, designed to be more transparent than the original. Premiums are used to purchase units (shares) of an investment fund, called the with-pro? t fund. As the fund earns investment return, the shares increase in value (or more shares are issued), increasing the bene? t entitlement as reversionary bonus.The shares will not decrease in value. On death or maturity, a further terminal bonus may be payable depending on the performance of the with-pro? t fund. After some poor publicity surrounding with-pro? t business, and, by association, unitized with-pro? t business, these product designs were withdrawn from the UK and Australian markets by the early 2000s. However, they will remain i mportant for many years as many companies carry very large portfolios of with-pro? t (traditional and unitized) policies issued during the second half of the twentieth century.Equity-linked insurance has a bene? t linked to the performance of an investment fund. There are two different forms. The ? rst is where the policyholder’s premiums are invested in an open-ended investment company style account; at maturity, the bene? t is the accumulated value of the premiums. There is a guaranteed minimum death bene? t payable if the policyholder dies before the contract matures. In some cases, there is also a guaranteed minimum maturity bene? t payable. In the UK and most of Europe, these are called unit-linked policies, and they rarely carry a guaranteed maturity bene? . In Canada they are known as segregated fund policies and always carry a maturity guarantee. In the USA these contracts are called variable annuity contracts; maturity guarantees are increasingly common for these pol icies. (The use of the term ‘annuity’ for these contracts is very misleading. The bene? ts are designed with a single lump sum payout, though there may be an option to convert the lump sum to an annuity. ) The second form of equity-linked insurance is the Equity-Indexed Annuity (EIA) in the USA.Under an EIA the policyholder is guaranteed a minimum return on their premium (minus an initial expense charge). At maturity, the policyholder receives a proportion of the return on a speci? ed stock index, if that is greater than the guaranteed minimum return. EIAs are generally rather shorter in term than unit-linked products, with seven-year policies being typical; variable annuity contracts commonly 8 Introduction to life insurance have terms of twenty years or more. EIAs are much less popular with consumers than variable annuities. 1. 3. 4 Distribution methods Most people ? d insurance dauntingly complex. Brokers who connect individuals to an appropriate insurance product ha ve, since the earliest times, played an important role in the market. There is an old saying amongst actuaries that ‘insurance is sold, not bought’, which means that the role of an intermediary in persuading potential policyholders to take out an insurance policy is crucial in maintaining an adequate volume of new business. Brokers, or other ? nancial advisors, are often remunerated through a commission system. The commission would be speci? ed as a percentage of the premium paid.Typically, there is a higher percentage paid on the ? rst premium than on subsequent premiums. This is referred to as a front-end load. Some advisors may be remunerated on a ? xed fee basis, or may be employed by one or more insurance companies on a salary basis. An alternative to the broker method of selling insurance is direct marketing. Insurers may use television advertising or other telemarketing methods to sell direct to the public. The nature of the business sold by direct marketing meth ods tends to differ from the broker sold business. For example, often the sum insured is smaller.The policy may be aimed at a niche market, such as older lives concerned with insurance to cover their own funeral expenses (called pre-need insurance in the USA). Another mass marketed insurance contract is loan or credit insurance, where an insurer might cover loan or credit card payments in the event of the borrower’s death, disability or unemployment. 1. 3. 5 Underwriting It is important in modelling life insurance liabilities to consider what happens when a life insurance policy is purchased. Selling life insurance policies is a competitive business and life insurance companies (also known as life of? es) are constantly considering ways in which to change their procedures so that they can improve the service to their customers and gain a commercial advantage over their competitors. The account given below of how policies are sold covers some essential points but is necessaril y a simpli? ed version of what actually happens. For a given type of policy, say a 10-year term insurance, the life of? ce will have a schedule of premium rates. These rates will depend on the size of the policy and some other factors known as rating factors.An applicant’s risk level is assessed by asking them to complete a proposal form giving information on 1. 3 Life insurance and annuity contracts 9 relevant rating factors, generally including their age, gender, smoking habits, occupation, any dangerous hobbies, and personal and family health history. The life insurer may ask for permission to contact the applicant’s doctor to enquire about their medical history. In some cases, particularly for very large sums insured, the life insurer may require that the applicant’s health be checked by a doctor employed by the insurer.The process of collecting and evaluating this information is called underwriting. The purpose of underwriting is, ? rst, to classify potenti al policyholders into broadly homogeneous risk categories, and secondly to assess what additional premium would be appropriate for applicants whose risk factors indicate that standard premium rates would be too low. On the basis of the application and supporting medical information, potential life insurance policyholders will generally be categorized into one of the following groups: †¢ Preferred lives have very low mortality risk based on the standard infor- mation.The preferred applicant would have no recent record of smoking; no evidence of drug or alcohol abuse; no high-risk hobbies or occupations; no family history of disease known to have a strong genetic component; no adverse medical indicators such as high blood pressure or cholesterol level or body mass index. The preferred life category is common in North America, but has not yet caught on elsewhere. In other areas there is no separation of preferred and normal lives. †¢ Normal lives may have some higher rated ri sk factors than preferred lives (where this category exists), but are still insurable at standard rates.Most applicants fall into this category. †¢ Rated lives have one or more risk factors at raised levels and so are not acceptable at standard premium rates. However, they can be insured for a higher premium. An example might be someone having a family history of heart disease. These lives might be individually assessed for the appropriate additional premium to be charged. This category would also include lives with hazardous jobs or hobbies which put them at increased risk. †¢ Uninsurable lives have such signi? ant risk that the insurer will not enter an insurance contract at any price. Within the ? rst three groups, applicants would be further categorized according to the relative values of the various risk factors, with the most fundamental being age, gender and smoking status. Most applicants (around 95% for traditional life insurance) will be accepted at preferred or standard rates for the relevant risk category. Another 2–3% may be accepted at non-standard rates 10 Introduction to life insurance because of an impairment, or a dangerous occupation, leaving around 2–3% who ill be refused insurance. The rigour of the underwriting process will depend on the type of insurance being purchased, on the sum insured and on the distribution process of the insurance company. Term insurance is generally more strictly underwritten than whole life insurance, as the risk taken by the insurer is greater. Under whole life insurance, the payment of the sum insured is certain, the uncertainty is in the timing. Under, say, 10-year term insurance, it is assumed that the majority of contracts will expire with no death bene? t paid.If the underwriting is not strict there is a risk of adverse selection by policyholders – that is, that very high-risk individuals will buy insurance in disproportionate numbers, leading to excessive losses. Since high sum insured contracts carry more risk than low sum insured, high sums insured would generally trigger more rigorous underwriting. The marketing method also affects the level of underwriting. Often, direct marketed contracts are sold with relatively low bene? t levels, and with the attraction that no medical evidence will be sought beyond a standard questionnaire.The insurer may assume relatively heavy mortality for these lives to compensate for potential adverse selection. By keeping the underwriting relatively light, the expenses of writing new business can be kept low, which is an attraction for high-volume, low sum insured contracts. It is interesting to note that with no third party medical evidence the insurer is placing a lot of weight on the veracity of the policyholder. Insurers have a phrase for this – that both insurer and policyholder may assume ‘utmost good faith’ or ‘uberrima ? es’ on the part of the other side of the contract. In practi ce, in the event of the death of the insured life, the insurer may investigate whether any pertinent information was withheld from the application. If it appears that the policyholder held back information, or submitted false or misleading information, the insurer may not pay the full sum insured. 1. 3. 6 Premiums A life insurance policy may involve a single premium, payable at the outset of the contract, or a regular series of premiums payable provided the policyholder survives, perhaps with a ? ed end date. In traditional contracts the regular premium is generally a level amount throughout the term of the contract; in more modern contracts the premium might be variable, at the policyholder’s discretion for investment products such as equity-linked insurance, or at the insurer’s discretion for certain types of term insurance. Regular premiums may be paid annually, semi-annually, quarterly, monthly or weekly. Monthly premiums are common as it is convenient for policyho lders to have their outgoings payable with approximately the same frequency as their income. . 3 Life insurance and annuity contracts 11 An important feature of all premiums is that they are paid at the start of each period. Suppose a policyholder contracts to pay annual premiums for a 10-year insurance contract. The premiums will be paid at the start of the contract, and then at the start of each subsequent year provided the policyholder is alive. So, if we count time in years from t = 0 at the start of the contract, the ? rst premium is paid at t = 0, the second is paid at t = 1, and so on, to the tenth premium paid at t = 9.Similarly, if the premiums are monthly, then the ? rst monthly instalment will be paid at t = 0, and the ? nal premium will be paid at the start 11 of the ? nal month at t = 9 12 years. (Throughout this book we assume that all 1 months are equal in length, at 12 years. ) 1. 3. 7 Life annuities Annuity contracts offer a regular series of payments. When an annui ty depends on the survival of the recipient, it is called a ‘life annuity’. The recipient is called an annuitant. If the annuity continues until the death of the annuitant, it is called a whole life annuity.If the annuity is paid for some maximum period, provided the annuitant survives that period, it is called a term life annuity. Annuities are often purchased by older lives to provide income in retirement. Buying a whole life annuity guarantees that the income will not run out before the annuitant dies. Single Premium Deferred Annuity (SPDA) Under an SPDA contract, the policyholder pays a single premium in return for an annuity which commences payment at some future, speci? ed date. The annuity is ‘life contingent’, by which we mean the annuity is paid only if the policyholder survives to the payment dates.If the policyholder dies before the annuity commences, there may be a death bene? t due. If the policyholder dies soon after the annuity commences, the re may be some minimum payment period, called the guarantee period, and the balance would be paid to the policyholder’s estate. Single Premium Immediate Annuity (SPIA) This contract is the same as the SPDA, except that the annuity commences as soon as the contract is effected. This might, for example, be used to convert a lump sum retirement bene? t into a life annuity to supplement a pension.As with the SPDA, there may be a guarantee period applying in the event of the early death of the annuitant. Regular Premium Deferred Annuity (RPDA) The RPDA offers a deferred life annuity with premiums paid through the deferred period. It is otherwise the same as the SPDA. Joint life annuity A joint life annuity is issued on two lives, typically a married couple. The annuity (which may be single premium or regular 12 Introduction to life insurance premium, immediate or deferred) continues while both lives survive, and ceases on the ? rst death of the couple.Last survivor annuity A last survivor annuity is similar to the joint life annuity, except that payment continues while at least one of the lives survives, and ceases on the second death of the couple. Reversionary annuity A reversionary annuity is contingent on two lives, usually a couple. One is designated as the annuitant, and one the insured. No annuity bene? t is paid while the insured life survives. On the death of the insured life, if the annuitant is still alive, the annuitant receives an annuity for the remainder of his or her life. 1. Other insurance contracts The insurance and annuity contracts described above are all contingent on death or survival. There are other life contingent risks, in particular involving shortterm or long-term disability. These are known as morbidity risks. Income protection insurance When a person becomes sick and cannot work, their income will, eventually, be affected. For someone in regular employment, the employer may cover salary for a period, but if the sickness continu es the salary will be decreased, and ultimately will stop being paid at all. For someone who is elf-employed, the effects of sickness on income will be immediate. Income protection policies replace at least some income during periods of sickness. They usually cease at retirement age. Critical illness insurance Some serious illnesses can cause signi? cant expense at the onset of the illness. The patient may have to leave employment, or alter their home, or incur severe medical expenses. Critical illness insurance pays a bene? t on diagnosis of one of a number of severe conditions, such as certain cancers or heart disease. The bene? t is usually in the form of a lump sum.Long-term care insurance This is purchased to cover the costs of care in old age, when the insured life is unable to continue living independently. The bene? t would be in the form of the long-term care costs, so is an annuity bene? t. 1. 5 Pension bene? ts Many actuaries work in the area of pension plan design, valua tion and risk management. The pension plan is usually sponsored by an employer. Pension plans typically offer employees (also called pension plan members) either lump 1. 5 Pension bene? ts 13 sums or annuity bene? ts or both on retirement, or deferred lump sum or annuity bene? s (or both) on earlier withdrawal. Some offer a lump sum bene? t if the employee dies while still employed. The bene? ts therefore depend on the survival and employment status of the member, and are quite similar in nature to life insurance bene? ts – that is, they involve investment of contributions long into the future to pay for future life contingent bene? ts. 1. 5. 1 De? ned bene? t and de? ned contribution pensions De? ned Bene? t (DB) pensions offer retirement income based on service and salary with an employer, using a de? ned formula to determine the pension.For example, suppose an employee reaches retirement age with n years of service (i. e. membership of the pension plan), and with pensionab le salary averaging S in, say, the ? nal three years of employment. A typical ? nal salary plan might offer an annual pension at retirement of B = Sn? , where ? is called the accrual rate, and is usually around 1%–2%. The formula may be interpreted as a pension bene? t of, say, 2% of the ? nal average salary for each year of service. The de? ned bene? t is funded by contributions paid by the employer and (usually) the employee over the working lifetime of the employee.The contributions are invested, and the accumulated contributions must be enough, on average, to pay the pensions when they become due. De? ned Contribution (DC) pensions work more like a bank account. The employee and employer pay a predetermined contribution (usually a ? xed percentage of salary) into a fund, and the fund earns interest. When the employee leaves or retires, the proceeds are available to provide income throughout retirement. In the UK most of the proceeds must be converted to an annuity.In the USA and Canada there are more options – the pensioner may draw funds to live on without necessarily purchasing an annuity from an insurance company. 1. 5. 2 De? ned bene? t pension design The age retirement pension described in the section above de? nes the pension payable from retirement in a standard ? nal salary plan. Career average salary plans are also common in some jurisdictions, where the bene? t formula is the same as the ? nal salary formula above, except that the average salary over the employee’s entire career is used in place of the ? nal salary. Many employees leave their jobs before they retire.A typical withdrawal bene? t would be a pension based on the same formula as the age retirement bene? t, but with the start date deferred until the employee reaches the normal retirement age. Employees may have the option of taking a lump sum with the 14 Introduction to life insurance same value as the deferred pension, which can be invested in the pension plan of the new employer. Some pension plans also offer death-in-service bene? ts, for employees who die during their period of employment. Such bene? ts might include a lump sum, often based on salary and sometimes service, as well as a pension for the employee’s spouse. . 6 Mutual and proprietary insurers A mutual insurance company is one that has no shareholders. The insurer is owned by the with-pro? t policyholders. All pro? ts are distributed to the with-pro? t policyholders through dividends or bonuses. A proprietary insurance company has shareholders, and usually has withpro? t policyholders as well. The participating policyholders are not owners, but have a speci? ed right to some of the pro? ts. Thus, in a proprietary insurer, the pro? ts must be shared in some predetermined proportion, between the shareholders and the with-pro? t policyholders.Many early life insurance companies were formed as mutual companies. More recently, in the UK, Canada and the USA, there has been a trend towards demutualization, which means the transition of a mutual company to a proprietary company, through issuing shares (or cash) to the with-pro? t policyholders. Although it would appear that a mutual insurer would have marketing advantages, as participating policyholders receive all the pro? ts and other bene? ts of ownership, the advantages cited by companies who have demutualized include increased ability to raise capital, clearer corporate structure and improved ef? iency. 1. 7 Typical problems We are concerned in this book with developing the mathematical models and techniques used by actuaries working in life insurance and pensions. The primary responsibility of the life insurance actuary is to maintain the solvency and pro? tability of the insurer. Premiums must be suf? cient to pay bene? ts; the assets held must be suf? cient to pay the contingent liabilities; bonuses to policyholders should be fair. Consider, for example, a whole life insurance contract issued to a life aged 50. The sum insured may not be paid for 30 years or more.The premiums paid over the period will be invested by the insurer to earn signi? cant interest; the accumulated premiums must be suf? cient to pay the bene? ts, on average. To ensure this, the actuary needs to model the survival probabilities of the policyholder, the investment returns likely to be earned and the expenses likely 1. 9 Exercises 15 to be incurred in maintaining the policy. The actuary may take into consideration the probability that the policyholder decides to terminate the contract early. The actuary may also consider the pro? tability requirements for the contract.Then, when all of these factors have been modelled, they must be combined to set a premium. Each year or so, the actuary must determine how much money the insurer or pension plan should hold to ensure that future liabilities will be covered with adequately high probability. This is called the valuation process. For with-pro? t insurance, the actuary must determine a suitable level of bonus. The problems are rather more complex if the insurance also covers morbidity risk, or involves several lives. All of these topics are covered in the following chapters.The actuary may also be involved in decisions about how the premiums are invested. It is vitally important that the insurer remains solvent, as the contracts are very long-term and insurers are responsible for protecting the ? nancial security of the general public. The way the underlying investments are selected can increase or mitigate the risk of insolvency. The precise selection of investments to manage the risk is particularly important where the contracts involve ? nancial guarantees. The pensions actuary working with de? ned bene? t pensions must determine appropriate contribution rates to meet the bene? s promised, using models that allow for the working patterns of the employees. Sometimes, the employer may want to change the bene? t structure, and the actu ary is responsible for assessing the cost and impact. When one company with a pension plan takes over another, the actuary must assist with determining the best way to allocate the assets from the two plans, and perhaps how to merge the bene? ts. 1. 8 Notes and further reading A number of essays describing actuarial practice can be found in Renn (ed. ) (1998). This book also provides both historical and more contemporary contexts for life contingencies.The original papers of Graunt and Halley are available online (and any search engine will ? nd them). Anyone interested in the history of probability and actuarial science will ? nd these interesting, and remarkably modern. 1. 9 Exercises Exercise 1. 1 Why do insurers generally require evidence of health from a person applying for life insurance but not for an annuity? 16 Introduction to life insurance Exercise 1. 2 Explain why an insurer might demand more rigorous evidence of a prospective policyholder’s health status for a te rm insurance than for a whole life insurance. Exercise 1. Explain why premiums are payable in advance, so that the ? rst premium is due now rather than in one year’s time. Exercise 1. 4 Lenders offering mortgages to home owners may require the borrower to purchase life insurance to cover the outstanding loan on the death of the borrower, even though the mortgaged property is the loan collateral. (a) Explain why the lender might require term insurance in this circumstance. (b) Describe how this term insurance might differ from the standard term insurance described in Section 1. 3. 2. (c) Can you see any problems with lenders demanding term insurance from borrowers?Exercise 1. 5 Describe the difference between a cash bonus and a reversionary bonus for with-pro? t whole life insurance. What are the advantages and disadvantages of each for (a) the insurer and (b) the policyholder? Exercise 1. 6 It is common for insurers to design whole life contracts with premiums payable only up to age 80. Why? Exercise 1. 7 Andrew is retired. He has no pension, but has capital of $500 000. He is considering the following options for using the money: (a) Purchase an annuity from an insurance company that will pay a level amount for the rest of his life. b) Purchase an annuity from an insurance company that will pay an amount that increases with the cost of living for the rest of his life. (c) Purchase a 20-year annuity certain. (d) Invest the capital and live on the interest income. (e) Invest the capital and draw $40 000 per year to live on. What are the advantages and disadvantages of each option? 2 Survival models 2. 1 Summary In this chapter we represent the future lifetime of an individual as a random variable, and show how probabilities of death or survival can be calculated under this framework.We then de? ne an important quantity known as the force of mortality, introduce some actuarial notation, and discuss some properties of the distribution of future lifetime. W e introduce the curtate future lifetime random variable. This is a function of the future lifetime random variable which represents the number of complete years of future life. We explain why this function is useful and derive its probability function. 2. 2 The future lifetime random variable In Chapter 1 we saw that many insurance policies provide a bene? t on the death of the policyholder.When an insurance company issues such a policy, the policyholder’s date of death is unknown, so the insurer does not know exactly when the death bene? t will be payable. In order to estimate the time at which a death bene? t is payable, the insurer needs a model of human mortality, from which probabilities of death at particular ages can be calculated, and this is the topic of this chapter. We start with some notation. Let (x) denote a life aged x, where x ? 0. The death of (x) can occur at any age greater than x, and we model the future lifetime of (x) by a continuous random variable whic h we denote by Tx .This means that x + Tx represents the age-at-death random variable for (x). Let Fx be the distribution function of Tx , so that Fx (t) = Pr[Tx ? t]. Then Fx (t) represents the probability that (x) does not survive beyond age x + t, and we refer to Fx as the lifetime distribution from age x. In many life 17 18 Survival models insurance problems we are interested in the probability of survival rather than death, and so we de? ne Sx as Sx (t) = 1 ? Fx (t) = Pr[Tx > t]. Thus, Sx (t) represents the probability that (x) survives for at least t years, and Sx is known as the survival function. Given our interpretation of the ollection of random variables {Tx }x? 0 as the future lifetimes of individuals, we need a connection between any pair of them. To see this, consider T0 and Tx for a particular individual who is now aged