Book description
Provides a comprehensive coverage of both the deterministic and stochastic models of life contingencies, risk theory, credibility theory, multistate models, and an introduction to modern mathematical ?nance.
New edition restructures the material to ?t into modern computational methods and provides several spreadsheet examples throughout.
Covers the syllabus for the Institute of Actuaries subject CT5, Contingencies
Includes new chapters covering stochastic investments returns, universal life insurance. Elements of option pricing and the BlackScholes formula will be introduced.
Table of contents
 Preface
 Acknowledgements
 About the companion website

Part I THE DETERMINISTIC LIFE CONTINGENCIES MODEL
 1 Introduction and motivation

2 The basic deterministic model
 2.1 Cash flows
 2.2 An analogy with currencies
 2.3 Discount functions
 2.4 Calculating the discount function
 2.5 Interest and discount rates
 2.6 Constant interest
 2.7 Values and actuarial equivalence
 2.8 Vector notation
 2.9 Regular pattern cash flows
 2.10 Balances and reserves
 2.11 Time shifting and the splitting identity
 *2.11 Change of discount function
 2.12 Internal rates of return
 *2.13 Forward prices and term structure
 2.14 Standard notation and terminology
 2.15 Spreadsheet calculations
 Notes and references
 Exercises
 3 The life table
 4 Life annuities

5 Life insurance
 5.1 Introduction
 5.2 Calculating life insurance premiums
 5.3 Types of life insurance
 5.4 Combined insurance–annuity benefits
 5.5 Insurances viewed as annuities
 5.6 Summary of formulas
 5.7 A general insurance–annuity identity
 5.8 Standard notation and terminology
 5.9 Spreadsheet applications
 Exercises

6 Insurance and annuity reserves
 6.1 Introduction to reserves
 6.2 The general pattern of reserves
 6.3 Recursion
 6.4 Detailed analysis of an insurance or annuity contract
 6.5 Bases for reserves
 6.6 Nonforfeiture values
 6.7 Policies involving a return of the reserve
 6.8 Premium difference and paidup formulas
 6.9 Standard notation and terminology
 6.10 Spreadsheet applications
 Exercises
 7 Fractional durations

8 Continuous payments
 8.1 Introduction to continuous annuities
 8.2 The force of discount
 8.3 The constant interest case
 8.4 Continuous life annuities
 8.5 The force of mortality
 8.6 Insurances payable at the moment of death
 8.7 Premiums and reserves
 8.8 The general insurance–annuity identity in the continuous case
 8.9 Differential equations for reserves
 8.10 Some examples of exact calculation
 8.11 Further approximations from the life table
 8.12 Standard actuarial notation and terminology
 Notes and references
 Exercises
 9 Select mortality

10 Multiplelife contracts
 10.1 Introduction
 10.2 The jointlife status
 10.3 Jointlife annuities and insurances
 10.4 Lastsurvivor annuities and insurances
 10.5 Moment of death insurances
 10.6 The general twolife annuity contract
 10.7 The general twolife insurance contract
 10.8 Contingent insurances
 10.9 Duration problems
 *10.10 Applications to annuity credit risk
 10.11 Standard notation and terminology
 10.12 Spreadsheet applications
 Notes and references
 Exercises
 11 Multipledecrement theory
 12 Expenses and profits
 *13 Specialized topics

Part II THE STOCHASTIC LIFE CONTINGENCIES MODEL

14 Survival distributions and failure times
 14.1 Introduction to survival distributions
 14.2 The discrete case
 14.3 The continuous case
 14.4 Examples
 14.5 Shifted distributions
 14.6 The standard approximation
 14.7 The stochastic life table
 14.8 Life expectancy in the stochastic model
 14.9 Stochastic interest rates
 Notes and references
 Exercises

15 The stochastic approach to insurance and annuities
 15.1 Introduction
 15.2 The stochastic approach to insurance benefits
 15.3 The stochastic approach to annuity benefits
 *15.4 Deferred contracts
 15.5 The stochastic approach to reserves
 15.6 The stochastic approach to premiums
 15.7 The variance of r L
 15.8 Standard notation and terminology
 Notes and references
 Exercises
 16 Simplifications under level benefit contracts
 17 The minimum failure time

14 Survival distributions and failure times

Part III ADVANCED STOCHASTIC MODELS
 18 An introduction to stochastic processes
 19 Multistate models

20 Introduction to the Mathematics of Financial Markets
 20.1 Introduction
 20.2 Modelling prices in financial markets
 20.3 Arbitrage
 20.4 Option contracts
 20.5 Option prices in the oneperiod binomial model
 20.6 The multiperiod binomial model
 20.7 American options
 20.8 A general financial market
 20.9 Arbitragefree condition
 20.10 Existence and uniqueness of riskneutral measures
 20.11 Completeness of markets
 20.12 The Black–Scholes–Merton formula
 20.13 Bond markets
 Notes and references
 Exercises

Part IV RISK THEORY

21 Compound distributions
 21.1 Introduction
 21.2 The mean and variance of S
 21.3 Generating functions
 21.4 Exact distribution of S
 21.5 Choosing a frequency distribution
 21.6 Choosing a severity distribution
 21.7 Handling the point mass at 0
 21.8 Counting claims of a particular type
 21.9 The sum of two compound Poisson distributions
 21.10 Deductibles and other modifications
 21.11 A recursion formula for S
 Notes and references
 Exercises
 22 Risk assessment
 23 Ruin models:
 24 Credibility theory:

21 Compound distributions
 Answers to exercises

Appendix A review of probability theory
 A.1 Sample spaces and probability measures
 A.2 Conditioning and independence
 A.3 Random variables
 A.4 Distributions
 A.5 Expectations and moments
 A.6 Expectation in terms of the distribution function
 A.7 Joint distributions
 A.8 Conditioning and independence for random variables
 A.9 Moment generating functions
 A.10 Probability generating functions
 A.11 Some standard distributions
 A.12 Convolution
 A.13 Mixtures
 References
 Notation index
 Index
 End User License Agreement
Product information
 Title: Fundamentals of Actuarial Mathematics, 3rd Edition
 Author(s):
 Release date: January 2015
 Publisher(s): Wiley
 ISBN: 9781118782460
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