Heriot-Watt University. M.Sc. in Actuarial Science. Life Insurance Mathematics I. Tutorial 5
|
|
- Darrell Flynn
- 8 years ago
- Views:
Transcription
1 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 an annuity of 1 per year continuously during any period of illness, and a sum assured of 1 on death. A premium of P per annum is payable continuously while healthy. Let V j (t) be the prospective policy value at age + t, conditional on then being in state j (j =, 1, 2). µ 1 = able 1 = ill µ 1 µ 2 2 = dead Figure 1: An illness-death model (a) State and prove the Kolmogorov equations for t p and t p 1. (b) Write down Thiele s differential equations for this model. (c) State what are the boundary conditions you would use in solving Thiele s differential equations.
2 2 2. (Ecel eercise): Consider the following (simplified) model, in which mortality has been ignored. µ 1 = able 1 = ill µ 1 Figure 2: A simplified illness-death model The transition intensities are given by: µ 1 = µ 1 =.5. (a) Write down the Kolmogorov equations for t p and t p 1. (b) Using an Euler scheme with step size h =.1 years, solve the Kolmogorov equations to find approimate values of t p 2 and t p 1 2 for t 1. (c) An insurance company sells a 1-year insurance policy to someone age 2. The benefit is a annuity at rate 1 per annum, payable while ill. Write down Thiele s equations for the statewise policy values V (t) and V 1 (t). (d) The actuary uses the above transition intensities and a force of interest δ =.5 per annum to calculate premiums and policy values. By trial and error, or otherwise, find the annual rate of premium such that V () =. (e) Eplain what is happening to V 1 (t) as t approaches 1 years. Is this good or bad? 3. Consider the model and insurance policy in Question 2. Define T i to be the random time of the ith transition in the policyholder s life history during the policy term, and let S i be the state entered in the ith transition (i = 1, 2,...). If the policyholder dies or the 1-year term ends before reaching the ith transition, define T i = and S i = 1. (a) List all possible life histories in which the policyholder makes, 1, 2 or 3 transitions during the policy term. (b) Write down epressions for the present value at t = of the premiums paid during each life history listed in (a). (c) Hence, write down the first four terms in an epression for the EPV at t = of the premiums paid. (d) Comment on how practical it is to use the random times at which events take place to compute EPVs in this model, compared with the numerical solution of Thiele s equations.
3 3 4. An insurance company uses the multiple state model shown below to calculate premiums for long-term care contracts: 1 = able µ 13 2 = mild µ 24 µ 14 4 = dead µ 34 3 = disabled (a) Derive a differential equation for the occupancy probability t p 11. (b) Show by direct substitution that that the following satisfies the differential equation derived in (a) as well as the boundary condition p 11 = 1: { = ep t } +r + µ 13 +r + µ 14 +rdr. 5. An insurance company uses the multiple state model shown below to calculate premiums for the following long-term care contract: Premiums: Payable continuously while in state 1 Benefits: 5% SA per annum payable continuously while in state 2 1% SA per annum payable continuously while in state 3 Waiver: Premiums are waived while benefits are payable. 1.Able µ 21 µ 14 2.Mild 4.Dead µ 24 µ 32 µ 34 3.Disabled
4 4 The company has estimated the transition probabilities for the above model as: [ 1 t ] 3 + t 1 t (1 t) + t = tp 21 = = t (1 t) 4 + t 1 tp 22 = [ 1 t ] 4 + t 1 1 tp 13 = t (1 t) 2 + t 1 tp 23 = t (1 t) 1 + t 1 where t p ij + t. is the probability that a life aged in state i will be in state j at age The company uses the following basis for calculating premiums: Basis: Transition probabilities: Force of interest: Epenses: Indeation: as given 5% per annum continuously 8% of all premiums paid Premiums and benefits indeed at 5% per annum continuously. Show that the equation of value for the above long-term care policy for a life aged and with an initial sum assured of rate B per annum is:.92 P 1 dt = B 2 1 where P is the initial annual premium rate. dt + B 1 tp 13 dt Hence, calculate the annual premium rate at outset for a life aged 6 for a contract with an initial sum assured of 1, per annum on the above basis.
5 5 6. An insurance company uses the multiple state model shown below to calculate premiums for long-term care contracts: 1.Able µ 14 2.Mild 4.Dead µ 24 µ 34 3.Disabled The insurance company uses the following constant values for the transition intensities: µ 14 =.1 µ 24 =.2 µ 34 =.4 =.25 =.5. (a) Show that Kolmogorov s differential equation for the occupancy probability is: d dt t p 12 = t p 11 t p 12 ( + µ 24 ). (b) Show, using an Euler scheme with step-size s and the formula above: sp 12 s. Hence, setting s = 1 year, calculate an approimate value of 1 p 12. (c) Taking the net step in the Euler scheme, derive an epression for 2s p 12. You are given that: { = ep t } +r + µ 14 +rdr. Hence, setting s =.5 year, calculate another approimate value of 1 p 12. (d) Calculate 1 p 12 eactly given that, if the transition intensities are constant, then: = + µ 14 µ 24 [ ] e (µ23 +µ 24 ) t e (µ12 +µ 14 ) t and compare it to your answers for (b) and (c) and comment. How could you improve the accuracy of Euler s method to get a more accurate solution? (No further calculations are required.) Numerical Solutions: Q.5 7, Q.6(b).25 Q.6(c) Q.6(d)
JANUARY 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 informationSOCIETY OF ACTUARIES. EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE WRITTEN-ANSWER QUESTIONS AND SOLUTIONS
SOCIETY OF ACTUARIES EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE WRITTEN-ANSWER QUESTIONS AND SOLUTIONS Questions February 12, 2015 In Questions 12, 13, and 19, the wording was changed slightly
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 information3 Life Insurance and Differential Equations
3 Life Insurance and Differential Equations 3.1 Model specification Ourmodelwasspecifiedbytheassumptionthattheremaininglifetimeatage xwasa randomvariable T x withacontinuousdistribution.thatdistributioniscompletelydescribed
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 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 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 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 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 informationINSTRUCTIONS TO CANDIDATES
Society of Actuaries Canadian Institute of Actuaries Exam MLC Models for Life Contingencies Friday, October 31, 2014 8:30 a.m. 12:45 p.m. MLC General Instructions 1. Write your candidate number here. Your
More informationMay 2012 Course MLC Examination, Problem No. 1 For a 2-year select and ultimate mortality model, you are given:
Solutions to the May 2012 Course MLC Examination by Krzysztof Ostaszewski, http://www.krzysio.net, krzysio@krzysio.net Copyright 2012 by Krzysztof Ostaszewski All rights reserved. No reproduction in any
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 informationNovember 2012 Course MLC Examination, Problem No. 1 For two lives, (80) and (90), with independent future lifetimes, you are given: k p 80+k
Solutions to the November 202 Course MLC Examination by Krzysztof Ostaszewski, http://www.krzysio.net, krzysio@krzysio.net Copyright 202 by Krzysztof Ostaszewski All rights reserved. No reproduction in
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 information4. Life Insurance Payments
4. Life Insurance Payments A life insurance premium must take into account the following factors 1. The amount to be paid upon the death of the insured person and its present value. 2. The distribution
More information6 Insurances on Joint Lives
6 Insurances on Joint Lives 6.1 Introduction Itiscommonforlifeinsurancepoliciesandannuitiestodependonthedeathorsurvivalof more than one life. For example: (i) Apolicywhichpaysamonthlybenefittoawifeorotherdependentsafterthedeathof
More informationMathematics of Risk. Introduction. Case Study #1 Personal Auto Insurance Pricing. Mathematical Concepts Illustrated. Background
Mathematics of Risk Introduction There are many mechanisms that individuals and organizations use to protect themselves against the risk of financial loss. Government organizations and public and private
More informationINSTITUTE OF ACTUARIES OF INDIA
INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 13 th May 2015 Subject CT5 General Insurance, Life and Health Contingencies Time allowed: Three Hours (10.30 13.30 Hrs) Total Marks: 100 INSTRUCTIONS TO THE
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 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 information9.3 OPERATIONS WITH RADICALS
9. Operations with Radicals (9 1) 87 9. OPERATIONS WITH RADICALS In this section Adding and Subtracting Radicals Multiplying Radicals Conjugates In this section we will use the ideas of Section 9.1 in
More informationSome Observations on Variance and Risk
Some Observations on Variance and Risk 1 Introduction By K.K.Dharni Pradip Kumar 1.1 In most actuarial contexts some or all of the cash flows in a contract are uncertain and depend on the death or survival
More informationTABLE OF CONTENTS. GENERAL AND HISTORICAL PREFACE iii SIXTH EDITION PREFACE v PART ONE: REVIEW AND BACKGROUND MATERIAL
TABLE OF CONTENTS GENERAL AND HISTORICAL PREFACE iii SIXTH EDITION PREFACE v PART ONE: REVIEW AND BACKGROUND MATERIAL CHAPTER ONE: REVIEW OF INTEREST THEORY 3 1.1 Interest Measures 3 1.2 Level Annuity
More informationEXAMINATION. 6 April 2005 (pm) Subject CT5 Contingencies Core Technical. Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE
Faculty of Actuaries Institute of Actuaries EXAMINATION 6 April 2005 (pm) Subject CT5 Contingencies Core Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Enter all the candidate and
More informationActuarial Society of India
Actuarial Society of India EXAMINATION 30 th October 2006 Subject ST1 Health and Care Insurance Specialist Technical Time allowed: Three hours (14.15* pm 17.30 pm) INSTRUCTIONS TO THE CANDIDATE 1. Enter
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 informationHUNTINGTON S DISEASE AND INSURANCE II: CRITICAL ILLNESS AND LIFE INSURANCE. abstract
1 HUNTINGTON S DISEASE AND INSURANCE II: CRITICAL ILLNESS AND LIFE INSURANCE By Cristina Gutiérrez and Angus Macdonald abstract In Part I we proposed a model of Huntington s disease (HD), a highly penetrant,
More information2.1 The Present Value of an Annuity
2.1 The Present Value of an Annuity One example of a fixed annuity is an agreement to pay someone a fixed amount x for N periods (commonly months or years), e.g. a fixed pension It is assumed that the
More information, plus the present value of the $1,000 received in 15 years, which is 1, 000(1 + i) 30. Hence the present value of the bond is = 1000 ;
2 Bond Prices A bond is a security which offers semi-annual* interest payments, at a rate r, for a fixed period of time, followed by a return of capital Suppose you purchase a $,000 utility bond, freshly
More informationPractical Example of a Split Benefit Accelerated Critical Illness Insurance Product
Practical Example of a Split Accelerated Critical Illness Insurance Product Anton Brink, Ph.D. RGA UK Services Limited Presentation Disclaimers: Contains all personal views based on external research These
More information15.1. Exact Differential Equations. Exact First-Order Equations. Exact Differential Equations Integrating Factors
SECTION 5. Eact First-Order Equations 09 SECTION 5. Eact First-Order Equations Eact Differential Equations Integrating Factors Eact Differential Equations In Section 5.6, ou studied applications of differential
More informationTaylor Polynomials. for each dollar that you invest, giving you an 11% profit.
Taylor Polynomials Question A broker offers you bonds at 90% of their face value. When you cash them in later at their full face value, what percentage profit will you make? Answer The answer is not 0%.
More informationProduct Pricing and Solvency Capital Requirements for Long-Term Care Insurance
Product Pricing and Solvency Capital Requirements for Long-Term Care Insurance Adam W. Shao, Michael Sherris, Joelle H. Fong ARC Centre of Excellence in Population Ageing Research (CEPAR) UNSW Australia
More informationFurther Topics in Actuarial Mathematics: Premium Reserves. Matthew Mikola
Further Topics in Actuarial Mathematics: Premium Reserves Matthew Mikola April 26, 2007 Contents 1 Introduction 1 1.1 Expected Loss...................................... 2 1.2 An Overview of the Project...............................
More informationPolynomial and Synthetic Division. Long Division of Polynomials. Example 1. 6x 2 7x 2 x 2) 19x 2 16x 4 6x3 12x 2 7x 2 16x 7x 2 14x. 2x 4.
_.qd /7/5 9: AM Page 5 Section.. Polynomial and Synthetic Division 5 Polynomial and Synthetic Division What you should learn Use long division to divide polynomials by other polynomials. Use synthetic
More informationEXAMINATIONS. 18 April 2000 (am) Subject 105 Actuarial Mathematics 1. Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE
Faculty of Actuaries Institute of Actuaries EXAMINATIONS 18 April 2000 (am) Subject 105 Actuarial Mathematics 1 Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Write your surname in full, the
More informationCurrent Situation and Actuarial Issues of Long-Term Care Insurance in Japan. Masato Tomihari Mitsui Sumitomo Insurance Company Limited,Tokyo,Japan
Current Situation and Actuarial Issues of Long-Term Care Insurance in Japan Masato Tomihari Mitsui Sumitomo Insurance Company Limited,Tokyo,Japan Before the main topics Restrictions on the sale of insurance
More informationHow To Calculate Netting Effects In Life Insurance
Making use of netting effects when composing life insurance contracts Marcus Christiansen Preprint Series: 21-13 Fakultät für Mathematik und Wirtschaftswissenschaften UNIVERSITÄT ULM Making use of netting
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 informationWe hope you will find this sample a useful supplement to your existing educational materials, and we look forward to receiving your comments.
To Teachers of Mathematics: Thank you for visiting the BeAnActuary.org booth at the annual meeting of the National Council of Teachers of Mathematics. BeAnActuary.org is sponsored by the Joint Career Encouragement
More informationPREMIUM AND BONUS. MODULE - 3 Practice of Life Insurance. Notes
4 PREMIUM AND BONUS 4.0 INTRODUCTION A insurance policy needs to be bought. This comes at a price which is known as premium. Premium is the consideration for covering of the risk of the insured. The insured
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/ 1/14 Level benefit insurance in the continuous case In this chapter,
More information1. Revision 2. Revision pv 3. - note that there are other equivalent formulae! 1 pv 16.5 4. A x A 1 x:n A 1
Tutorial 1 1. Revision 2. Revision pv 3. - note that there are other equivalent formulae! 1 pv 16.5 4. A x A 1 x:n A 1 x:n a x a x:n n a x 5. K x = int[t x ] - or, as an approximation: T x K x + 1 2 6.
More informationINSTITUTE AND FACULTY OF ACTUARIES EXAMINATION
INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION 30 April 2015 (am) Subject SA2 Life Insurance Specialist Applications Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Enter all the candidate and
More informationGlossary of insurance terms
Glossary of insurance terms I. Insurance Products Annuity is a life insurance policy where an insurance company pays an income stream to an individual, usually until death, in exchange for the payment
More informationARC Centre of Excellence in Population Ageing Research. Working Paper 2015/03
ARC Centre of Ecellence in Population Ageing Research Working Paper 2015/03 Actuarial Values for Long-term Care Insurance Products. A Sensitivity Analysis Ermanno Pitacco * * Professor, University of Trieste,
More informationValuation Report on Prudential Annuities Limited as at 31 December 2003. The investigation relates to 31 December 2003.
PRUDENTIAL ANNUITIES LIMITED Returns for the year ended 31 December 2003 SCHEDULE 4 Valuation Report on Prudential Annuities Limited as at 31 December 2003 1. Date of investigation The investigation relates
More information1 st December 2014. Taxability of Life Insurance Benefits An Actuarial View
1 st December 2014 Taxability of Life Insurance Benefits An Actuarial View 1) The Finance Act 2014, has introduced Section 194 (DA) in the Income tax Act, 1961, requiring deduction of tax at source at
More informationHedging Variable Annuity Guarantees
p. 1/4 Hedging Variable Annuity Guarantees Actuarial Society of Hong Kong Hong Kong, July 30 Phelim P Boyle Wilfrid Laurier University Thanks to Yan Liu and Adam Kolkiewicz for useful discussions. p. 2/4
More informationComplex Genetic Risk: The Implications for Insurance
Complex Genetic Risk: The Implications for Insurance Angus Macdonald Heriot-Watt University, Edinburgh The Maxwell Institute for Mathematical Sciences Indeed, the sociology of risk... is an academic subject
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 informationEDUCATION AND EXAMINATION COMMITTEE SOCIETY OF ACTUARIES RISK AND INSURANCE. Copyright 2005 by the Society of Actuaries
EDUCATION AND EXAMINATION COMMITTEE OF THE SOCIET OF ACTUARIES RISK AND INSURANCE by Judy Feldman Anderson, FSA and Robert L. Brown, FSA Copyright 25 by the Society of Actuaries The Education and Examination
More informationMortgage Decreasing Term Assurance Plan
IMPORTANT INFORMATION This information may be downloaded to your PC in whole or in part provided that any reproduction or copy, or any derivative, is true to the original, and is EITHER used for personal
More informationASSUMPTION LIFE PARPLUS. Participating Whole Life Insurance
ASSUMPTION LIFE PARPLUS Participating Whole Life Insurance Features Issue ages Premium payment period Minimum sum insured Maximum sum insured Banding Annual fees Guaranteed cash values Riders Dividend
More informationTHE GENETICS OF BREAST AND OVARIAN CANCER V: APPLICATION TO INCOME PROTECTION INSURANCE. By Baopeng Lu, Angus Macdonald and Howard Waters.
1 THE GENETICS OF BREAST AND OVARIAN CANCER V: APPLICATION TO INCOME PROTECTION INSURANCE By Baopeng Lu, Angus Macdonald and Howard Waters abstract In Part IV we presented a comprehensive model of a life
More informationImpact of Genetic Testing on Life Insurance
Agenda, Volume 10, Number 1, 2003, pages 61-72 Impact of Genetic Testing on Life Insurance he Human Genome project generates immense interest in the scientific community though there are also important
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 informationFlexible Life Plan Key Features
Flexible Life Plan Flexible Life Plan Key Features This document shows the main points about your plan. Please read it with your personal illustration and keep it with the other documents relating to your
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 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 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 informationTHE SINE PRODUCT FORMULA AND THE GAMMA FUNCTION
THE SINE PRODUCT FORMULA AND THE GAMMA FUNCTION ERICA CHAN DECEMBER 2, 2006 Abstract. The function sin is very important in mathematics and has many applications. In addition to its series epansion, it
More informationLIFE INSURANCE AND PENSIONS by Peter Tryfos York University
LIFE INSURANCE AND PENSIONS by Peter Tryfos York University Introduction Life insurance is the business of insuring human life: in return for a premium payable in one sum or installments, an insurance
More informationDelme John Pritchard
THE GENETICS OF ALZHEIMER S DISEASE, MODELLING DISABILITY AND ADVERSE SELECTION IN THE LONGTERM CARE INSURANCE MARKET By Delme John Pritchard Submitted for the Degree of Doctor of Philosophy at HeriotWatt
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 informationPayment streams and variable interest rates
Chapter 4 Payment streams and variable interest rates In this chapter we consider two extensions of the theory Firstly, we look at payment streams A payment stream is a payment that occurs continuously,
More informationAT A GLANCE. Partner Oasis Buy-Out. Individual critical illness insurance
CRITICAL INDIVIDUAL ILLNESS DISABILITY INSURANCE INSURANCE AT A GLANCE Partner Oasis Buy-Out Individual critical illness insurance AT A GLANCE Table of Contents Partner Buy-Out..................................1
More informationHomework 2 Solutions
Homework Solutions Igor Yanovsky Math 5B TA Section 5.3, Problem b: Use Taylor s method of order two to approximate the solution for the following initial-value problem: y = + t y, t 3, y =, with h = 0.5.
More informationMath 370, Spring 2008 Prof. A.J. Hildebrand. Practice Test 1 Solutions
Math 70, Spring 008 Prof. A.J. Hildebrand Practice Test Solutions About this test. This is a practice test made up of a random collection of 5 problems from past Course /P actuarial exams. Most of the
More informationFive 5. Rational Expressions and Equations C H A P T E R
Five C H A P T E R Rational Epressions and Equations. Rational Epressions and Functions. Multiplication and Division of Rational Epressions. Addition and Subtraction of Rational Epressions.4 Comple Fractions.
More informationb g is the future lifetime random variable.
**BEGINNING OF EXAMINATION** 1. Given: (i) e o 0 = 5 (ii) l = ω, 0 ω (iii) is the future lifetime random variable. T Calculate Var Tb10g. (A) 65 (B) 93 (C) 133 (D) 178 (E) 333 COURSE/EXAM 3: MAY 000-1
More informationA Guide to Approved Retirement Funds (ARF)
& Guidance RF A Guide to Approved Retirement Funds (ARF) A Guide to Approved Retirement Funds Contents I m approaching retirement, what are my financial options? 02 What is a Financial Broker? 03 Why would
More informationMath 370/408, Spring 2008 Prof. A.J. Hildebrand. Actuarial Exam Practice Problem Set 2 Solutions
Math 70/408, Spring 2008 Prof. A.J. Hildebrand Actuarial Exam Practice Problem Set 2 Solutions About this problem set: These are problems from Course /P actuarial exams that I have collected over the years,
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 informationEARLY-ONSET ALZHEIMER S DISEASE, CRITICAL ILLNESS INSURANCE AND LIFE INSURANCE. By Eng Hock Gui and Angus Macdonald. abstract.
1 EARLY-ONSET ALZHEIMER S DISEASE, CRITICAL ILLNESS INSURANCE AND LIFE INSURANCE By Eng Hock Gui and Angus Macdonald abstract Early-onset Alzheimer s disease (EOAD) is a disorder with a dominantly inherited
More informationContinuous Compounding and Discounting
Continuous Compounding and Discounting Philip A. Viton October 5, 2011 Continuous October 5, 2011 1 / 19 Introduction Most real-world project analysis is carried out as we ve been doing it, with the present
More informationINDIVIDUAL DISABILITY INSURANCE
Disability Insurance Crash Course 1 AN INTRO TO INDIVIDUAL DISABILITY INSURANCE Disability Insurance Crash Course 2 AN INTRODUCTORY GUIDE TO HOW INDIVIDUAL DISABILITY INSURANCE POLICIES WORK, AND WHY YOU
More informationMarket Value of Insurance Contracts with Profit Sharing 1
Market Value of Insurance Contracts with Profit Sharing 1 Pieter Bouwknegt Nationale-Nederlanden Actuarial Dept PO Box 796 3000 AT Rotterdam The Netherlands Tel: (31)10-513 1326 Fax: (31)10-513 0120 E-mail:
More informationINCOME WHEN YOU ARE ILL
INCOME WHEN YOU ARE ILL Income protection insurance (IPI) or permanent health insurance (PHI) is an insurance that virtually everyone who works needs, but very few people have. One of the reasons for this
More informationDraft Guidance - Revenue & Customs Brief 04/13
Draft Guidance - Revenue & Customs Brief 04/13 Payments made or benefits provided by fund managers, fund platforms (fund supermarkets), advisers or other intermediaries to investors Following Revenue &
More informationNEW JERSEY FORM REQUIREMENTS INDIVIDUAL GENERAL ACCOUNT ANNUITIES
INDIVIDUAL GENERAL ACCOUNT ANNUITIES The same contract form shall not be issued as both an immediate and a deferred annuity. An annuity form shall not be identified as a single premium contract if it contains
More informationNo one likes to think about the possibility of being seriously injured in an accident or becoming too ill to work. But it can happen to any of us.
Insurance Planning One financial aspects of partnership is insurance 1. Disability insurance 2. Life insurance 3. Professional liability insurance Your law firm may have an established insurance package,
More informationChapter 2 Premiums and Reserves in Multiple Decrement Model
Chapter 2 Premiums and Reserves in Multiple Decrement Model 2.1 Introduction A guiding principle in the determination of premiums for a variety of life insurance products is: Expected present value of
More informationD1.03: MORTGAGE REPAYMENT OVERVIEW
D1.03: MORTGAGE REPAYMENT OVERVIEW SYLLABUS Repayment mortgages Repayment profile Interest only mortgages Full and low cost endowment mortgages Unit-linked endowment mortgages ISA mortgages Pension mortgages
More informationHomework 2 Solutions
Homework Solutions 1. (a) Find the area of a regular heagon inscribed in a circle of radius 1. Then, find the area of a regular heagon circumscribed about a circle of radius 1. Use these calculations to
More information6. Debt Valuation and the Cost of Capital
6. Debt Valuation and the Cost of Capital Introduction Firms rarely finance capital projects by equity alone. They utilise long and short term funds from a variety of sources at a variety of costs. No
More informationA, we round the female and male entry ages and
Pricing Practices for Joint Last Survivor Insurance Heekyung Youn Arkady Shemyakin University of St. Thomas unded by the Society of Actuaries Abstract In pricing joint last survivor insurance policies,
More informationThe Malaysian Insurance Institute
The Malaysian Insurance Institute (35445-H) 88 Life Assurance Objectives: To provide a knowledge and understanding of the scope of life assurance, its appropriate use and administration and the legal and
More informationA GUIDE TO RETIREMENT ANNUITY TRUST SCHEMES ( RATS ) IN GUERNSEY
A GUIDE TO RETIREMENT ANNUITY TRUST SCHEMES ( RATS ) IN GUERNSEY TABLE OF CONTENTS INTRODUCTION... 3 WHAT IS A RETIREMENT ANNUITY TRUST SCHEME?... 3 THE TRUSTEES... 4 APPROVAL... 4 TRANSFERS FROM OTHER
More informationSURRENDER VALUE AND PAID-UP VALUE STANDARD FOR LIFE INSURANCE
Actuarial Society of Malaysia (ASM) SURRENDER VALUE AND PAID-UP VALUE STANDARD FOR LIFE INSURANCE Prepared by: Life Insurance Sub-Committee of Actuarial Society of Malaysia TABLE OF CONTENTS CONTENTS PAGE
More informationProtect your home and family today. Client Brochure Policy Series 174
Protect your home and family today. Client Brochure Policy Series 174 Your home may be your most valuable asset... Provide peace of mind when you and your family need it most. Many families are forced
More informationTaxation of Non-Registered Enriched (or Impaired) Annuities
Taxation of Non-Registered Enriched (or Impaired) Annuities In addition to having a bearing on longevity, an individual s medical history can result in that individual being rated, which can translate
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 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 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 informationLife Insurance Modelling: Notes for teachers. Overview
Life Insurance Modelling: Notes for teachers In this mathematics activity, students model the following situation: An investment fund is set up Investors pay a set amount at the beginning of 20 years.
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 informationNATIONAL INSURANCE COMMISSION GUIDELINES ON APPLICATIONS FOR APPROVAL OF NEW AND REPACKAGED LIFE INSURANCE PRODUCTS
NATIONAL INSURANCE COMMISSION GUIDELINES ON APPLICATIONS FOR APPROVAL OF NEW AND REPACKAGED LIFE INSURANCE PRODUCTS 1.0 INTRODUCTION In a bid to protect policyholders, section 45 of Insurance Act, 2006
More informationChapter 9 Experience rating
0 INTRODUCTION 1 Chapter 9 Experience rating 0 Introduction The rating process is the process of deciding on an appropriate level of premium for a particular class of insurance business. The contents of
More information