About the companion website
by S. David Promislow
Fundamentals of Actuarial Mathematics, 3rd Edition
- 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 paid-up 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 Multiple-life contracts
- 10.1 Introduction
- 10.2 The joint-life status
- 10.3 Joint-life annuities and insurances
- 10.4 Last-survivor annuities and insurances
- 10.5 Moment of death insurances
- 10.6 The general two-life annuity contract
- 10.7 The general two-life 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 Multiple-decrement 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 Multi-state 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 one-period binomial model
- 20.6 The multi-period binomial model
- 20.7 American options
- 20.8 A general financial market
- 20.9 Arbitrage-free condition
- 20.10 Existence and uniqueness of risk-neutral 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
About the companion website
This book is accompanied by a companion website:
www.wiley.com/go/promislow/actuarial
The website includes:
- A variety of exercises, both computational and theoretical
- Answers, enabling use for self-study.
-
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