Mathematics of Life Contingencies. Math W Instructor: Edward Furman Homework 1
|
|
- Myron Lang
- 8 years ago
- Views:
Transcription
1 Mathematics of Life Contingencies. Math W Instructor: Edward Furman Homework 1 Unless otherwise indicated, all lives in the following questions are subject to the same law of mortality and their times until death are independent random variables. 1. Assume that a decision maker s current wealth is 10,000. Assign u(0)=-1 and u(10,000)=0. a) When facing a loss of X with probability 0.5 and remaining at current wealth with probability 0.5, the decision maker would be willing to pay up to G for complete insurance. The values for X and G in three situations are given below. X G Determine three values on the decision maker s utility of wealth function u. b) Calculate the slopes of the four line segments joining the five points determined on the graph u(w). Determine the rates of change of the slopes from segment to segment. c) Put yourself in the role of a decision maker with wealth 10,000. In additional to the given values of u(0) and u(10,000), elicit three additional values on your utility of wealth function u. d) On the basis of the five values of your utility function, calculate the slopes and the rates of change of the slopes as done in part (b). 1
2 2. Consider a game of chance that consists of tossing a coin until a head appears. The probability of a head is 0.5 and the repeated trails are independent. Let the random variable N be the number of the trial on which the first head occurs. a) Show that the probability function of N is given by f(n) = ( 1 2 )n n = 1, 2, 3, b) Find E[N] and Var(N). c) If a reward of X = 2 N is paid, prove that the expectation of the reward does not exist. d) If this reward has utility u(w)=log w, find E[u(X)]. 3. A utility function is given by e (w 100)2 /200 w < 100 u(w) = 2 e (w 100)2 /200 w 100 a) Is u (w) 0? b) For what range of w is u (w) < 0? 4. If a utility function is such that u (w) > 0 and u (w) > 0, show that π[x] E[X]. A decision maker with preferences consistent with u (w) > 0 is a risk lover. 5. You are given: 1) The benefit of 1 on a ten-year endowment insurance is payable at the moment of death, or at the end of 10 years if (x) survives 10 years. 2) µ x (t) = 0.01 for t > 0. 3) δ =
3 Determine the single benefit premium. Note that under constant force of mortality, the expectation of random variable for 1 unit of whole life insurance is µ µ+δ. A x:10 = µ µ + δ (1 e n(µ+δ) ) + e n(µ+δ) = A whole life insurance pays a benefit of 10e 0.05t at the moment of death if death occurs at time t. You are given: 1) µ = ) δ = 0.04 Calculate the actuarial present value of the benefit. Netting the 0.05 rate of benefit increase against δ = 0.04 yields a net interest rate of Letting A be the actuarial present value of the benefit, ( ) 0.02 A = 10 = An n-year term insurance payable at the moment of death has actuarial present value of You are given: 1) µ x (t) = 0.007, t > 0. 2) δ = Determine n. We have = µ µ + δ (1 e n(µ+δ) ) = (1 e 0.057n ) n = 11 3
4 8. For a whole life insurance of 1000 on (x) with benefits payable at the moment of death: < t 10 1) δ t = < t < t 10 2) µ x (t) = < t Calculate the single benefit premium for this insurance. The single benefit premium for 1 is A x = A1 x: E x A x+10 = A x (1 10 E x ) + 10 E x A x+10 = Therefore, the single benefit premium for a benefit of 1000 is Dave wants to purchase a 5 year pure endowment with a single benefit premium. The amount of the endowment is $1,000. His insurance agent convinces him instead to use the same money to purchase a year endowment insurance policy which pays at the moment of death or at the end of five years, whichever comes first. You are given that µ = 0.04 and δ = Calculate the benefit amount for this 5 year endowment. A x: 1 5 = e 5( ) = , whereas A x:5 = (1 e 0.5 ) + e 0.5 = , so the benefit amount for endowment insurance is 100( / ) =
5 10. Bryon, a non-actuary, estimates the single benefit premium for a continuous whole life policy with a benefit of $100,000 on (30) by calculating the present value of $100,000 paid at the expected time of death. (30) is subject to a constant force of mortality µ x = 0.05, and the force of interest is δ = Determine the absolute value of the error of Bryon s estimate. The expected value of an exponential distribution is the reciprocal of the force, or 1/0.05=20. The value of $100,000 paid in 20 years is 100, 000e 20(0.08) =100, 000e 1.6 = , 190. The true value of 100, 000A 30 is 100, 000( ) = 38, 462. The error is $18, Given: 1) i=5%. 2) The force of mortality is constant. 3) e x = 16 Calculate 20 A x. The mean survival time is 16, so the force of mortality is 1/16. Under the constant force of mortality, A x+20 = A x. Thus we have: ( ) 20 A x = 20 E x A x = e (ln1.05+1/16)(20) 1/16 1/16 + ln1.05 = For a continuous whole life insurance (Z = v T, T 0), E[Z]=0.25. Assume the forces of mortality and interest are each constant. Calculate Var(Z). 5
6 Since E[Z]=µ/µ + δ = 0.25, it follows that δ = 3µ. Then, E[Z 2 ] = µ µ + 2δ = 1/7 V ar(z) = 1 7 (1 4 )2 = Z is the present-value random variable for a whole life insurance of b payable at the moment of death of (x). You are given: 1) µ x+t = 0.01, t 0 2) δ = ) The single benefit premium for this insurance is equal to Var(Z). Calculate b. For one unit, E[Z]= µ µ+δ = 1 6 and V ar(z) = µ µ + 2δ (E[Z])2 = So we need b such that b 6 = 25b2 396 b = = 2.64 GOOD LUCK! 6
Manual for SOA Exam MLC.
Chapter 4. Life Insurance. Extract from: Arcones Manual for the SOA Exam MLC. Fall 2009 Edition. available at http://www.actexmadriver.com/ 1/14 Level benefit insurance in the continuous case In this chapter,
More informationJANUARY 2016 EXAMINATIONS. Life Insurance I
PAPER CODE NO. MATH 273 EXAMINER: Dr. C. Boado-Penas TEL.NO. 44026 DEPARTMENT: Mathematical Sciences JANUARY 2016 EXAMINATIONS Life Insurance I Time allowed: Two and a half hours INSTRUCTIONS TO CANDIDATES:
More informationManual for SOA Exam MLC.
Chapter 4. Life insurance. Extract from: Arcones Fall 2009 Edition, available at http://www.actexmadriver.com/ (#1, Exam M, Fall 2005) For a special whole life insurance on (x), you are given: (i) Z is
More informationMATH 3630 Actuarial Mathematics I Class Test 2 Wednesday, 17 November 2010 Time Allowed: 1 hour Total Marks: 100 points
MATH 3630 Actuarial Mathematics I Class Test 2 Wednesday, 17 November 2010 Time Allowed: 1 hour Total Marks: 100 points Please write your name and student number at the spaces provided: Name: Student ID:
More informationMath 630 Problem Set 2
Math 63 Problem Set 2 1. AN n-year term insurance payable at the moment of death has an actuarial present value (i.e. EPV) of.572. Given µ x+t =.7 and δ =.5, find n. (Answer: 11) 2. Given: Ā 1 x:n =.4275,
More informationPremium Calculation. Lecture: Weeks 12-14. Lecture: Weeks 12-14 (Math 3630) Annuities Fall 2015 - Valdez 1 / 32
Premium Calculation Lecture: Weeks 12-14 Lecture: Weeks 12-14 (Math 3630) Annuities Fall 2015 - Valdez 1 / 32 Preliminaries Preliminaries An insurance policy (life insurance or life annuity) is funded
More informationHow To Perform The Mathematician'S Test On The Mathematically Based Test
MATH 3630 Actuarial Mathematics I Final Examination - sec 001 Monday, 10 December 2012 Time Allowed: 2 hours (6:00-8:00 pm) Room: MSB 411 Total Marks: 120 points Please write your name and student number
More informationMathematics of Life Contingencies MATH 3281
Mathematics of Life Contingencies MATH 3281 Life annuities contracts Edward Furman Department of Mathematics and Statistics York University February 13, 2012 Edward Furman Mathematics of Life Contingencies
More informationInsurance Benefits. Lecture: Weeks 6-8. Lecture: Weeks 6-8 (STT 455) Insurance Benefits Fall 2014 - Valdez 1 / 36
Insurance Benefits Lecture: Weeks 6-8 Lecture: Weeks 6-8 (STT 455) Insurance Benefits Fall 2014 - Valdez 1 / 36 An introduction An introduction Central theme: to quantify the value today of a (random)
More information4. Life Insurance. 4.1 Survival Distribution And Life Tables. Introduction. X, Age-at-death. T (x), time-until-death
4. Life Insurance 4.1 Survival Distribution And Life Tables Introduction X, Age-at-death T (x), time-until-death Life Table Engineers use life tables to study the reliability of complex mechanical and
More informationPremium calculation. summer semester 2013/2014. Technical University of Ostrava Faculty of Economics department of Finance
Technical University of Ostrava Faculty of Economics department of Finance summer semester 2013/2014 Content 1 Fundamentals Insurer s expenses 2 Equivalence principles Calculation principles 3 Equivalence
More informationManual for SOA Exam MLC.
Chapter 4. Life Insurance. c 29. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam MLC. Fall 29 Edition. available at http://www.actexmadriver.com/ c 29. Miguel A. Arcones.
More informationManual for SOA Exam MLC.
Chapter 5. Life annuities. Extract from: Arcones Manual for the SOA Exam MLC. Spring 2010 Edition. available at http://www.actexmadriver.com/ 1/114 Whole life annuity A whole life annuity is a series of
More informationACTS 4301 FORMULA SUMMARY Lesson 1: Probability Review. Name f(x) F (x) E[X] Var(X) Name f(x) E[X] Var(X) p x (1 p) m x mp mp(1 p)
ACTS 431 FORMULA SUMMARY Lesson 1: Probability Review 1. VarX)= E[X 2 ]- E[X] 2 2. V arax + by ) = a 2 V arx) + 2abCovX, Y ) + b 2 V ary ) 3. V ar X) = V arx) n 4. E X [X] = E Y [E X [X Y ]] Double expectation
More informationEXAM 3, FALL 003 Please note: On a one-time basis, the CAS is releasing annotated solutions to Fall 003 Examination 3 as a study aid to candidates. It is anticipated that for future sittings, only the
More informationSOCIETY OF ACTUARIES. EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE QUESTIONS The following questions or solutions have been modified since this document was prepared to use with the syllabus effective
More informationPremium Calculation. Lecture: Weeks 12-14. Lecture: Weeks 12-14 (STT 455) Premium Calculation Fall 2014 - Valdez 1 / 31
Premium Calculation Lecture: Weeks 12-14 Lecture: Weeks 12-14 (STT 455) Premium Calculation Fall 2014 - Valdez 1 / 31 Preliminaries Preliminaries An insurance policy (life insurance or life annuity) is
More informationAnnuities. Lecture: Weeks 9-11. Lecture: Weeks 9-11 (STT 455) Annuities Fall 2014 - Valdez 1 / 43
Annuities Lecture: Weeks 9-11 Lecture: Weeks 9-11 (STT 455) Annuities Fall 2014 - Valdez 1 / 43 What are annuities? What are annuities? An annuity is a series of payments that could vary according to:
More informationTABLE OF CONTENTS. 4. Daniel Markov 1 173
TABLE OF CONTENTS 1. Survival A. Time of Death for a Person Aged x 1 B. Force of Mortality 7 C. Life Tables and the Deterministic Survivorship Group 19 D. Life Table Characteristics: Expectation of Life
More informationHeriot-Watt University. BSc in Actuarial Mathematics and Statistics. Life Insurance Mathematics I. Extra Problems: Multiple Choice
Heriot-Watt University BSc in Actuarial Mathematics and Statistics Life Insurance Mathematics I Extra Problems: Multiple Choice These problems have been taken from Faculty and Institute of Actuaries exams.
More informationMath 425 (Fall 08) Solutions Midterm 2 November 6, 2008
Math 425 (Fall 8) Solutions Midterm 2 November 6, 28 (5 pts) Compute E[X] and Var[X] for i) X a random variable that takes the values, 2, 3 with probabilities.2,.5,.3; ii) X a random variable with the
More informationManual for SOA Exam MLC.
Chapter 5. Life annuities Extract from: Arcones Fall 2009 Edition, available at http://www.actexmadriver.com/ 1/60 (#24, Exam M, Fall 2005) For a special increasing whole life annuity-due on (40), you
More informationPremium Calculation - continued
Premium Calculation - continued Lecture: Weeks 1-2 Lecture: Weeks 1-2 (STT 456) Premium Calculation Spring 2015 - Valdez 1 / 16 Recall some preliminaries Recall some preliminaries An insurance policy (life
More informationSOCIETY OF ACTUARIES. EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE QUESTIONS The following questions or solutions have been modified since this document was prepared to use with the syllabus effective
More informationA LOGNORMAL MODEL FOR INSURANCE CLAIMS DATA
REVSTAT Statistical Journal Volume 4, Number 2, June 2006, 131 142 A LOGNORMAL MODEL FOR INSURANCE CLAIMS DATA Authors: Daiane Aparecida Zuanetti Departamento de Estatística, Universidade Federal de São
More informationManual for SOA Exam MLC.
Chapter 5 Life annuities Extract from: Arcones Manual for the SOA Exam MLC Fall 2009 Edition available at http://wwwactexmadrivercom/ 1/94 Due n year temporary annuity Definition 1 A due n year term annuity
More information3 Introduction to Assessing Risk
3 Introduction to Assessing Risk Important Question. How do we assess the risk an investor faces when choosing among assets? In this discussion we examine how an investor would assess the risk associated
More informationActuarial mathematics 2
Actuarial mathematics 2 Life insurance contracts Edward Furman Department of Mathematics and Statistics York University January 3, 212 Edward Furman Actuarial mathematics MATH 328 1 / 45 Definition.1 (Life
More informationFINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA
FINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA 1.1 Solve linear equations and equations that lead to linear equations. a) Solve the equation: 1 (x + 5) 4 = 1 (2x 1) 2 3 b) Solve the equation: 3x
More informationManual for SOA Exam MLC.
Chapter 6. Benefit premiums. Extract from: Arcones Fall 2010 Edition, available at http://www.actexmadriver.com/ 1/77 Fully discrete benefit premiums In this section, we will consider the funding of insurance
More information3. The Economics of Insurance
3. The Economics of Insurance Insurance is designed to protect against serious financial reversals that result from random evens intruding on the plan of individuals. Limitations on Insurance Protection
More informationManual for SOA Exam MLC.
Chapter 4. Life Insurance. Extract from: Arcones Manual for the SOA Exam MLC. Fall 2009 Edition. available at http://www.actexmadriver.com/ 1/44 Properties of the APV for continuous insurance The following
More informationSOCIETY OF ACTUARIES EXAM M ACTUARIAL MODELS EXAM M SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM M ACTUARIAL MODELS EXAM M SAMPLE QUESTIONS Copyright 005 by the Society of Actuaries Some of the questions in this study note are taken from past SOA examinations. M-09-05 PRINTED
More informationSolution. Let us write s for the policy year. Then the mortality rate during year s is q 30+s 1. q 30+s 1
Solutions to the May 213 Course MLC Examination by Krzysztof Ostaszewski, http://wwwkrzysionet, krzysio@krzysionet Copyright 213 by Krzysztof Ostaszewski All rights reserved No reproduction in any form
More informationChapter 4 Lecture Notes
Chapter 4 Lecture Notes Random Variables October 27, 2015 1 Section 4.1 Random Variables A random variable is typically a real-valued function defined on the sample space of some experiment. For instance,
More information1. Datsenka Dog Insurance Company has developed the following mortality table for dogs:
1 Datsenka Dog Insurance Company has developed the following mortality table for dogs: Age l Age l 0 2000 5 1200 1 1950 6 1000 2 1850 7 700 3 1600 8 300 4 1400 9 0 Datsenka sells an whole life annuity
More informationGenerating Random Data. Alan T. Arnholt Department of Mathematical Sciences Appalachian State University arnholt@math.appstate.edu
Generating Random Data Alan T. Arnholt Department of Mathematical Sciences Appalachian State University arnholt@math.appstate.edu Spring 2006 R Notes 1 Copyright c 2006 Alan T. Arnholt 2 Generating Random
More informationHealth insurance pricing in Spain: Consequences and alternatives
Health insurance pricing in Spain: Consequences and alternatives Anna Castañer, M. Mercè Claramunt and Carmen Ribas Dept. Matemàtica Econòmica, Financera i Actuarial Universitat de Barcelona Abstract For
More informationManual for SOA Exam MLC.
Manual for SOA Eam MLC. Chapter 4. Life Insurance. Etract from: Arcones Manual for the SOA Eam MLC. Fall 2009 Edition. available at http://www.actemadriver.com/ Manual for SOA Eam MLC. 1/9 Payments at
More informationO MIA-009 (F2F) : GENERAL INSURANCE, LIFE AND
No. of Printed Pages : 11 MIA-009 (F2F) kr) ki) M.Sc. ACTUARIAL SCIENCE (MSCAS) N December, 2012 0 O MIA-009 (F2F) : GENERAL INSURANCE, LIFE AND HEALTH CONTINGENCIES Time : 3 hours Maximum Marks : 100
More information1 Cash-flows, discounting, interest rate models
Assignment 1 BS4a Actuarial Science Oxford MT 2014 1 1 Cash-flows, discounting, interest rate models Please hand in your answers to questions 3, 4, 5 and 8 for marking. The rest are for further practice.
More informationSOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM C CONSTRUCTION AND EVALUATION OF ACTUARIAL MODELS EXAM C SAMPLE QUESTIONS
SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM C CONSTRUCTION AND EVALUATION OF ACTUARIAL MODELS EXAM C SAMPLE QUESTIONS Copyright 005 by the Society of Actuaries and the Casualty Actuarial Society
More informationLecture 10 - Risk and Insurance
Lecture 10 - Risk and Insurance 14.03 Spring 2003 1 Risk Aversion and Insurance: Introduction To have a passably usable model of choice, we need to be able to say something about how risk affects choice
More informationStatistics 100A Homework 4 Solutions
Problem 1 For a discrete random variable X, Statistics 100A Homework 4 Solutions Ryan Rosario Note that all of the problems below as you to prove the statement. We are proving the properties of epectation
More informationFinal Mathematics 5010, Section 1, Fall 2004 Instructor: D.A. Levin
Final Mathematics 51, Section 1, Fall 24 Instructor: D.A. Levin Name YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT. A CORRECT ANSWER WITHOUT SHOWING YOUR REASONING WILL NOT RECEIVE CREDIT. Problem Points Possible
More informationINSTITUTE AND FACULTY OF ACTUARIES EXAMINATION
INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION 27 April 2015 (pm) Subject CT5 Contingencies Core Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Enter all the candidate and examination
More informationarxiv:1112.0829v1 [math.pr] 5 Dec 2011
How Not to Win a Million Dollars: A Counterexample to a Conjecture of L. Breiman Thomas P. Hayes arxiv:1112.0829v1 [math.pr] 5 Dec 2011 Abstract Consider a gambling game in which we are allowed to repeatedly
More informationManual for SOA Exam MLC.
Chapter 6. Benefit premiums Extract from: Arcones Fall 2010 Edition, available at http://www.actexmadriver.com/ 1/90 (#4, Exam M, Spring 2005) For a fully discrete whole life insurance of 100,000 on (35)
More informationINSTITUTE OF ACTUARIES OF INDIA
INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 17 th November 2011 Subject CT5 General Insurance, Life and Health Contingencies Time allowed: Three Hours (10.00 13.00 Hrs) Total Marks: 100 INSTRUCTIONS TO
More informationManual for SOA Exam MLC.
Chapter 6. Benefit premiums. Extract from: Arcones Fall 2010 Edition, available at http://www.actexmadriver.com/ 1/24 Non-level premiums and/or benefits. Let b k be the benefit paid by an insurance company
More informationProperties of Future Lifetime Distributions and Estimation
Properties of Future Lifetime Distributions and Estimation Harmanpreet Singh Kapoor and Kanchan Jain Abstract Distributional properties of continuous future lifetime of an individual aged x have been studied.
More informationSOA EXAM MLC & CAS EXAM 3L STUDY SUPPLEMENT
SOA EXAM MLC & CAS EXAM 3L STUDY SUPPLEMENT by Paul H. Johnson, Jr., PhD. Last Modified: October 2012 A document prepared by the author as study materials for the Midwestern Actuarial Forum s Exam Preparation
More informationACTUARIAL MATHEMATICS FOR LIFE CONTINGENT RISKS
ACTUARIAL MATHEMATICS FOR LIFE CONTINGENT RISKS DAVID C. M. DICKSON University of Melbourne MARY R. HARDY University of Waterloo, Ontario V HOWARD R. WATERS Heriot-Watt University, Edinburgh CAMBRIDGE
More informationINSTITUTE AND FACULTY OF ACTUARIES EXAMINATION
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION 8 October 2015 (pm) Subject CT5 Contingencies Core Technical
More informationExact Confidence Intervals
Math 541: Statistical Theory II Instructor: Songfeng Zheng Exact Confidence Intervals Confidence intervals provide an alternative to using an estimator ˆθ when we wish to estimate an unknown parameter
More informationHomework # 3 Solutions
Homework # 3 Solutions February, 200 Solution (2.3.5). Noting that and ( + 3 x) x 8 = + 3 x) by Equation (2.3.) x 8 x 8 = + 3 8 by Equations (2.3.7) and (2.3.0) =3 x 8 6x2 + x 3 ) = 2 + 6x 2 + x 3 x 8
More informationAP CALCULUS AB 2007 SCORING GUIDELINES (Form B)
AP CALCULUS AB 2007 SCORING GUIDELINES (Form B) Question 4 Let f be a function defined on the closed interval 5 x 5 with f ( 1) = 3. The graph of f, the derivative of f, consists of two semicircles and
More information.4 120 +.1 80 +.5 100 = 48 + 8 + 50 = 106.
Chapter 16. Risk and Uncertainty Part A 2009, Kwan Choi Expected Value X i = outcome i, p i = probability of X i EV = pix For instance, suppose a person has an idle fund, $100, for one month, and is considering
More informationManual for SOA Exam MLC.
Chapter 5 Life annuities Extract from: Arcones Manual for the SOA Exam MLC Fall 2009 Edition available at http://wwwactexmadrivercom/ 1/70 Due n year deferred annuity Definition 1 A due n year deferred
More informationHYPOTHESIS TESTING: POWER OF THE TEST
HYPOTHESIS TESTING: POWER OF THE TEST The first 6 steps of the 9-step test of hypothesis are called "the test". These steps are not dependent on the observed data values. When planning a research project,
More informationIntermediate Micro. Expected Utility
Intermediate Micro Expected Utility Workhorse model of intermediate micro Utility maximization problem Consumers Max U(x,y) subject to the budget constraint, I=P x x + P y y Health Economics Spring 2015
More informationSection 5.1 Continuous Random Variables: Introduction
Section 5. Continuous Random Variables: Introduction Not all random variables are discrete. For example:. Waiting times for anything (train, arrival of customer, production of mrna molecule from gene,
More information2 Policy Values and Reserves
2 Policy Values and Reserves [Handout to accompany this section: reprint of Life Insurance, from The Encyclopaedia of Actuarial Science, John Wiley, Chichester, 2004.] 2.1 The Life Office s Balance Sheet
More information~ EQUIVALENT FORMS ~
~ EQUIVALENT FORMS ~ Critical to understanding mathematics is the concept of equivalent forms. Equivalent forms are used throughout this course. Throughout mathematics one encounters equivalent forms of
More information[Source: Added at 17 Ok Reg 1659, eff 7-14-00]
TITLE 365. INSURANCE DEPARTMENT CHAPTER 10. LIFE, ACCIDENT AND HEALTH SUBCHAPTER 17. VALUATION OF LIFE INSURANCE POLICIES REGULATION INCLUDING THE INTRODUCTION AND USE OF NEW SELECT MORTALITY FACTORS)
More informationChapter 2. 1. You are given: 1 t. Calculate: f. Pr[ T0
Chapter 2 1. You are given: 1 5 t F0 ( t) 1 1,0 t 125 125 Calculate: a. S () t 0 b. Pr[ T0 t] c. Pr[ T0 t] d. S () t e. Probability that a newborn will live to age 25. f. Probability that a person age
More informationErrata and updates for ASM Exam C/Exam 4 Manual (Sixteenth Edition) sorted by page
Errata for ASM Exam C/4 Study Manual (Sixteenth Edition) Sorted by Page 1 Errata and updates for ASM Exam C/Exam 4 Manual (Sixteenth Edition) sorted by page Practice exam 1:9, 1:22, 1:29, 9:5, and 10:8
More informationMath 431 An Introduction to Probability. Final Exam Solutions
Math 43 An Introduction to Probability Final Eam Solutions. A continuous random variable X has cdf a for 0, F () = for 0 <
More informationAMS 5 CHANCE VARIABILITY
AMS 5 CHANCE VARIABILITY The Law of Averages When tossing a fair coin the chances of tails and heads are the same: 50% and 50%. So if the coin is tossed a large number of times, the number of heads and
More informationBA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420
BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420 1. Which of the following will increase the value of the power in a statistical test
More informationUniversity of California, Los Angeles Department of Statistics. Random variables
University of California, Los Angeles Department of Statistics Statistics Instructor: Nicolas Christou Random variables Discrete random variables. Continuous random variables. Discrete random variables.
More informationMortality Risk and its Effect on Shortfall and Risk Management in Life Insurance
Mortality Risk and its Effect on Shortfall and Risk Management in Life Insurance AFIR 2011 Colloquium, Madrid June 22 nd, 2011 Nadine Gatzert and Hannah Wesker University of Erlangen-Nürnberg 2 Introduction
More informationIntroduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 4.4 Homework
Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 4.4 Homework 4.65 You buy a hot stock for $1000. The stock either gains 30% or loses 25% each day, each with probability.
More informationXII. RISK-SPREADING VIA FINANCIAL INTERMEDIATION: LIFE INSURANCE
XII. RIS-SPREADIG VIA FIACIAL ITERMEDIATIO: LIFE ISURACE As discussed briefly at the end of Section V, financial assets can be traded directly in the capital markets or indirectly through financial intermediaries.
More informationA Uniform Asymptotic Estimate for Discounted Aggregate Claims with Subexponential Tails
12th International Congress on Insurance: Mathematics and Economics July 16-18, 2008 A Uniform Asymptotic Estimate for Discounted Aggregate Claims with Subexponential Tails XUEMIAO HAO (Based on a joint
More informationLectures 5-6: Taylor Series
Math 1d Instructor: Padraic Bartlett Lectures 5-: Taylor Series Weeks 5- Caltech 213 1 Taylor Polynomials and Series As we saw in week 4, power series are remarkably nice objects to work with. In particular,
More informationCHAPTER 45-04-12 VALUATION OF LIFE INSURANCE POLICIES
CHAPTER 45-04-12 VALUATION OF LIFE INSURANCE POLICIES Section 45-04-12-01 Applicability 45-04-12-02 Definitions 45-04-12-03 General Calculation Requirements for Basic Reserves and Premium Deficiency Reserves
More informationA SURVEY ON CONTINUOUS ELLIPTICAL VECTOR DISTRIBUTIONS
A SURVEY ON CONTINUOUS ELLIPTICAL VECTOR DISTRIBUTIONS Eusebio GÓMEZ, Miguel A. GÓMEZ-VILLEGAS and J. Miguel MARÍN Abstract In this paper it is taken up a revision and characterization of the class of
More informationStatistics 100A Homework 8 Solutions
Part : Chapter 7 Statistics A Homework 8 Solutions Ryan Rosario. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, the one-half
More informationBinomial random variables
Binomial and Poisson Random Variables Solutions STAT-UB.0103 Statistics for Business Control and Regression Models Binomial random variables 1. A certain coin has a 5% of landing heads, and a 75% chance
More informationHeriot-Watt University. M.Sc. in Actuarial Science. Life Insurance Mathematics I. Tutorial 5
1 Heriot-Watt University M.Sc. in Actuarial Science Life Insurance Mathematics I Tutorial 5 1. Consider the illness-death model in Figure 1. A life age takes out a policy with a term of n years that pays
More informationBinomial random variables (Review)
Poisson / Empirical Rule Approximations / Hypergeometric Solutions STAT-UB.3 Statistics for Business Control and Regression Models Binomial random variables (Review. Suppose that you are rolling a die
More informationValuation of the Minimum Guaranteed Return Embedded in Life Insurance Products
Financial Institutions Center Valuation of the Minimum Guaranteed Return Embedded in Life Insurance Products by Knut K. Aase Svein-Arne Persson 96-20 THE WHARTON FINANCIAL INSTITUTIONS CENTER The Wharton
More informationNormal distribution. ) 2 /2σ. 2π σ
Normal distribution The normal distribution is the most widely known and used of all distributions. Because the normal distribution approximates many natural phenomena so well, it has developed into a
More informationEconomics 206 Problem Set 1 Winter 2007 Vincent Crawford
Economics 206 Problem Set 1 Winter 2007 Vincent Crawford This problem set, which is optional, covers the material in the first half of the course, roughly in the order in which topics are discussed in
More informationGLOSSARY. A contract that provides for periodic payments to an annuitant for a specified period of time, often until the annuitant s death.
The glossary contains explanations of certain terms and definitions used in this prospectus in connection with the Group and its business. The terms and their meanings may not correspond to standard industry
More informationValuation of the Surrender Option Embedded in Equity-Linked Life Insurance. Brennan Schwartz (1976,1979) Brennan Schwartz
Valuation of the Surrender Option Embedded in Equity-Linked Life Insurance Brennan Schwartz (976,979) Brennan Schwartz 04 2005 6. Introduction Compared to traditional insurance products, one distinguishing
More informationVALUATION OF LIFE INSURANCE POLICIES MODEL REGULATION (Including the Introduction and Use of New Select Mortality Factors)
Table of Contents Model Regulation Service October 2009 VALUATION OF LIFE INSURANCE POLICIES MODEL REGULATION (Including the Introduction and Use of New Select Mortality Factors) Section 1. Section 2.
More informationBiometrical worst-case and best-case scenarios in life insurance
Biometrical worst-case and best-case scenarios in life insurance Marcus C. Christiansen 8th Scientific Conference of the DGVFM April 30, 2009 Solvency Capital Requirement: The Standard Formula Calculation
More informationפרויקט מסכם לתואר בוגר במדעים )B.Sc( במתמטיקה שימושית
המחלקה למתמטיקה Department of Mathematics פרויקט מסכם לתואר בוגר במדעים )B.Sc( במתמטיקה שימושית הימורים אופטימליים ע"י שימוש בקריטריון קלי אלון תושיה Optimal betting using the Kelly Criterion Alon Tushia
More informationPractice Exam 1. x l x d x 50 1000 20 51 52 35 53 37
Practice Eam. You are given: (i) The following life table. (ii) 2q 52.758. l d 5 2 5 52 35 53 37 Determine d 5. (A) 2 (B) 2 (C) 22 (D) 24 (E) 26 2. For a Continuing Care Retirement Community, you are given
More informationMATH 10: Elementary Statistics and Probability Chapter 5: Continuous Random Variables
MATH 10: Elementary Statistics and Probability Chapter 5: Continuous Random Variables Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of slides,
More informationSolution. Solution. (a) Sum of probabilities = 1 (Verify) (b) (see graph) Chapter 4 (Sections 4.3-4.4) Homework Solutions. Section 4.
Math 115 N. Psomas Chapter 4 (Sections 4.3-4.4) Homework s Section 4.3 4.53 Discrete or continuous. In each of the following situations decide if the random variable is discrete or continuous and give
More informationNORTH CAROLINA GENERAL ASSEMBLY 1981 SESSION CHAPTER 761 SENATE BILL 623
NORTH CAROLINA GENERAL ASSEMBLY 1981 SESSION CHAPTER 761 SENATE BILL 623 AN ACT TO AMEND CHAPTER 58, ARTICLE 22, OF THE GENERAL STATUTES RELATING TO NONFORFEITURE BENEFITS OF LIFE INSURANCE POLICIES AND
More informationChoice Under Uncertainty
Decision Making Under Uncertainty Choice Under Uncertainty Econ 422: Investment, Capital & Finance University of ashington Summer 2006 August 15, 2006 Course Chronology: 1. Intertemporal Choice: Exchange
More informationA linear algebraic method for pricing temporary life annuities
A linear algebraic method for pricing temporary life annuities P. Date (joint work with R. Mamon, L. Jalen and I.C. Wang) Department of Mathematical Sciences, Brunel University, London Outline Introduction
More informationT H~ purpose of this note is to outline a rather simple technique that
TRANSACTIONS OF SOCIETY OF ACTUARIES 1960 VOL. 12 NO. 34 REFUND ANNUITIES WITHOUT "TRIAL AND ERROR"--ACTUARIAL NOTE DONALD H. REID T H~ purpose of this note is to outline a rather simple technique that
More informationMath 202-0 Quizzes Winter 2009
Quiz : Basic Probability Ten Scrabble tiles are placed in a bag Four of the tiles have the letter printed on them, and there are two tiles each with the letters B, C and D on them (a) Suppose one tile
More information