Actuarial Mathematics for Life Contingent Risks

ISBN-10: 0521118255
ISBN-13: 9780521118255
Edition: 2009
List price: $97.95
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Book details

List price: $97.95
Copyright year: 2009
Publisher: Cambridge University Press
Publication date: 9/24/2009
Binding: Hardcover
Pages: 508
Size: 6.25" wide x 9.50" long x 1.25" tall
Weight: 2.046
Language: English

Deborah J. Yashar is Associate Professor of Politics and International Affairs at Princeton University. She is the author of Demanding Democracy: Reform and Reaction in Costa Rica and Guatemala, 1870s-1950s (Stanford University Press) as well as articles and chapters on democratization, ethnic politics, collective action, and globalization.Deborah J. Yashar is Associate Professor of Politics and International Affairs at Princeton University. She is the author of Demanding Democracy: Reform and Reaction in Costa Rica and Guatemala, 1870s-1950s (Stanford University Press) as well as articles and chapters on democratization, ethnic politics, collective action, and globalization.David C. M. Dickson is a Professor in Actuarial Studies in the Department of Economics at the University of Melbourne. He is also Adjunct Professor in the Department of Statistics and Actuarial Science at the University of Waterloo.

Mary R. Hardy holds the CIBC Chair in Financial Risk Management at the University of Waterloo, Ontario. She is a Fellow of the UK Institute of Actuaries and of the Society of Actuaries, and has won awards and commendations for her research from the International Actuarial Association, the Institute of Actuaries and the Society of Actuaries.

Howard Waters is Professor in the Department of Actuarial Mathematics and Statistics at Heriot-Watt University, Edinburgh. He is a Fellow of the Faculty of Actuaries and the Institute of Actuaries, by whom he was awarded the Finlaison Medal for 'Services to the Actuarial Profession' in 2006.

Preface
Introduction to life insurance
Summary
Background
Life insurance and annuity contracts
Introduction
Traditional insurance contracts
Modern insurance contracts
Distribution methods
Underwriting
Premiums
Life annuities
Other insurance contracts
Pension benefits
Defined benefit and defined contribution pensions
Defined benefit pension design
Mutual and proprietary insurers
Typical problems
Notes and further reading
Exercises
Survival models
Summary
The future lifetime random variable
The force of mortality
Actuarial notation
Mean and standard deviation of T<sub>x</sub>
Curtate future lifetime
K<sub>x</sub> and e<sub>x</sub>
The complete and curtate expected future lifetimes, e<sub>x</sub> and e<sub>x</sub>
Notes and further reading
Exercises
Life tables and selection
Summary
Life tables
Fractional age assumptions
Uniform distribution of deaths
Constant force of mortality
National life tables
Survival models for life insurance policyholders
Life insurance underwriting
Select and ultimate survival models
Notation and formulae for select survival models
Select life tables
Notes and further reading
Exercises
Insurance benefits
Summary
Introduction
Assumptions
Valuation of insurance benefits
Whole life insurance: the continuous case, &Abar;<sub>x</sub>
Whole life insurance: the annual case, A<sub>x</sub>
Whole life insurance: the 1 /mthly case, A<sup>(m)</sup><sub>x</sub>
Recursions
Term insurance
Pure endowment
Endowment insurance
Deferred insurance benefits
Relating &Abar;<sub>x</sub>, A<sub>x</sub> and A<sup>(m)</sup><sub>x</sub>
Using the uniform distribution of deaths assumption
Using the claims acceleration approach
Variable insurance benefits
Functions for select lives
Notes and further reading
Exercises
Annuities
Summary
Introduction
Review of annuities-certain
Annual life annuities
Whole life annuity-due
Term annuity-due
Whole life immediate annuity
Term immediate annuity
Annuities payable continuously
Whole life continuous annuity
Term continuous annuity
Annuities payable m times per year
Introduction
Life annuities payable m times a year
Term annuities payable m times a year
Comparison of annuities by payment frequency
Deferred annuities
Guaranteed annuities
Increasing annuities
Arithmetically increasing annuities
Geometrically increasing annuities
Evaluating annuity functions
Recursions
Applying the UDD assumption
Woolhouse's formula
Numerical illustrations
Functions for select lives
Notes and further reading
Exercises
Premium calculation
Summary
Preliminaries
Assumptions
The present value of future loss random variable
The equivalence principle
Net premiums
Gross premium calculation
Profit
The portfolio percentile premium principle
Extra risks
Age rating
Constant addition to �x
Constant multiple of mortality rates
Notes and further reading
Exercises
Policy values
Summary
Assumptions
Policies with annual cash flows
The future loss random variable
Policy values for policies with annual cash flows
Recursive formulae for policy values
Annual profit
Asset shares
Policy values for policies with cash flows at discrete intervals other than annually
Recursions
Valuation between premium dates
Policy values with continuous cash flows
Thiele's differential equation
Numerical solution of Thiele's differential equation
Policy alterations
Retrospective policy value
Negative policy values
Notes and further reading
Exercises
Multiple state models
Summary
Examples of multiple state models
The alive-dead model
Term insurance with increased benefit on accidental death
The permanent disability model
The disability income insurance model
The joint life and last survivor model
Assumptions and notation
Formulae for probabilities
Kolmogorov's forward equations
Numerical evaluation of probabilities
Premiums
Policy values and Thiele's differential equation
The disability income model
Thiele's differential equation - the general case
Multiple decrement models
Joint life and last survivor benefits
The model and assumptions
Joint life and last survivor probabilities
Joint life and last survivor annuity and insurance functions
An important special case: independent survival models
Transitions at specified ages
Notes and further reading
Exercises
Pension mathematics
Summary
Introduction
The salary scale function
Setting the DC contribution
The service table
Valuation of benefits
Final salary plans
Career average earnings plans
Funding plans
Notes and further reading
Exercises
Interest rate risk
Summary
The yield curve
Valuation of insurances and life annuities
Replicating the cash flows of a traditional non-participating product
Diversifiable and non-diversifiable risk
Diversifiable mortality risk
Non-diversifiable risk
Monte Carlo simulation
Notes and further reading
Exercised
Emerging costs for traditional life insurance
Summary
Profit testing for traditional life insurance
The net cash flows for a policy
Reserves
Profit measures
A further example of a profit test
Notes and further reading
Exercises
Emerging costs for equity-linked insurance
Summary
Equity-linked insurance
Deterministic profit testing for equity-linked insurance
Stochastic profit testing
Stochastic pricing
Stochastic reserving
Reserving for policies with non-diversifiable risk
Quantile reserving
CTE reserving
Comments on reserving
Notes and further reading
Exercises
Option pricing
Summary
Introduction
The'no arbitrage�assumption
Options
The binomial option pricing model
Assumptions
Pricing over a single time period
Pricing over two time periods
Summary of the binomial model option pricing technique
The Black-Scholes-Merton model
The model
The Black-Scholes-Merton option pricing formula
Notes and further reading
Exercises
Embedded options
Summary
Introduction
Guaranteed minimum maturity benefit
Pricing
Reserving
Guaranteed minimum death benefit
Pricing
Reserving
Pricing methods for embedded options
Risk management
Emerging costs
Notes and further reading
Exercises
Probability theory
Probability distributions
Binomial distribution
Uniform distribution
Normal distribution
Lognormal distribution
The central limit theorem
Functions of a random variable
Discrete random variables
Continuous random variables
Mixed random variables
Conditional expectation and conditional variance
Notes and further reading
Numerical techniques
Numerical integration
The trapezium rule
Repeated Simpson's rule
Integrals over an infinite interval
Woolhouse's formula
Notes and further reading
Simulation
The inverse transform method
Simulation from a normal distribution
The Box-Muller method
The polar method
Notes and further reading
References
Author index
Index

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