Fundamentals of Actuarial Mathematics

ISBN-10: 0470684119

ISBN-13: 9780470684115

Edition: 2nd 2011

Authors: S. David Promislow

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Description:

The book is an introduction to actuarial mathematics and features new topics including an introduction to time diagrams and credibility theory, multi-state models and continuous time models. More complex types of contingent insurances will be featured and will include cases which involve durations or benefit amounts contingent on the time of the first death and will include applications on credit risk in life annuities. An introduction, without too much technical material, will be featured on flexible contracts such as universal life, and variable annuities and will include some discussion of the techniques of cash flow analysis and scenario testing. Percentile premiums will be introduced and the general concepts of VAR and conditional tail expectation will be discussed.
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Book details

Edition: 2nd
Copyright year: 2011
Publisher: John Wiley & Sons, Limited
Publication date: 12/10/2010
Binding: Hardcover
Pages: 476
Size: 8.50" wide x 9.50" long x 1.00" tall
Weight: 2.134
Language: English

Preface
Notation index
The Deterministic Model
Introduction and motivation
Risk and insurance
Deterministic versus stochastic models
Finance and investments
Adequacy and equity
Reassessment
Conclusion
The basic deterministic model
Cashflows
An analogy with currencies
Discount functions
Calculating the discount function
Interest and discount rates
Constant interest
Values and actuarial equivalence
Regular pattern cashflows
Balances and reserves
Time shifting and the splitting identity
Change of discount function
Internal rate of return
Forward prices and term structure
Standard notation and terminology
Spreadsheet calculations
Notes and references
Exercises
The life table
Basic definitions
Probabilities
Constructing the life table from the values of q x
Life expectancy
Choice of life tables
Standard notation and terminology
A sample table
Notes and references
Exercises
Life annuities
Introduction
Calculating annuity premiums
The interest and survivorship discount function
Guaranteed payments
Deferred annuities with annual premiums
Some practical considerations
Standard notation and terminology
Spreadsheet calculations
Exercises
Life insurance
Introduction
Calculating life insurance premiums
Types of life insurance
Combined insurance-annuity benefits
Insurances viewed as annuities
Summary of formulas
A general insurance–annuity identity
Standard notation and terminology
Spreadsheet applications
Exercises
Insurance and annuity reserves
Introduction to reserves
The general pattern of reserves
Recursion
Detailed analysis of an insurance or annuity contract
Interest and mortality bases for reserves
Non forfeiture values
Policies involving a ‘return of the reserve'
Universal life and variables annuities
Standard notation and terminology
Spreadsheet applications
Exercises
Fractional durations
Introduction
Cashflows discounted with interest only
Life annuities paid mthly
Immediate annuities
Approximation and computation
Fractional period premiums and reserves
Reserves at fractional durations
Notes and references
Exercises
Continuous payments
Introduction to continuous annuities
The force of discount
The constant interest case
Continuous life annuities
The force of mortality
Insurances payable at the moment of death
Premiums and reserves
The general insurance–annuity identity in the continuous case
Differential equations for reserves
Some examples of exact calculation
Standard notation and terminology
Notes and references
Exercises
Select mortality
Introduction
Select and ultimate tables
Changes in formulas
Projections in annuity tables
Further remarks
Exercises
Multiple-life contracts
Introduction
The joint-life status
Joint-life annuities and insurances
Last-survivor annuities and insurances
Moment of death insurances
The general two-life annuity contract
The general two-life insurance contract
Contingent insurances
Duration problems
Applications to annuity credit risk
Standard notation and terminology
Spreadsheet applications
Notes and references
Exercises
Multiple-decrement theory
Introduction
The basic model
Insurances
Determining the model from the forces of decrement
The analogy with joint-life statuses
A machine analogy
Associated single-decrement tables
Notes and references
Exercises
Expenses
Introduction
Effect on reserves
Realistic reserve and balance calculations
Notes and references
Exercises
The Stochastic Model
Survival distributions and failure times
Introduction to survival distributions
The discrete case
The continuous case
Examples
Shifted distributions
The standard approximation
The stochastic life table
Life expectancy in the stochastic model
Stochastic interest rates
Notes and references
Exercises
The stochastic approach to insurance and annuities
Introduction
The stochastic approach to insurance benefits
The stochastic approach to annuity benefits
Deferred contracts
The stochastic approach to reserves
The stochastic approach to premiums
The variance of r L
Standard notation and terminology
Notes and references
Exercises
Simplifications under level benefit contracts
Introduction
Variance calculations in the continuous case
Variance calculations in the discrete case
Exact distributions
Non-level benefit examples
Exercises
The minimum failure time
Introduction
Joint distributions
The distribution of T
The joint distribution of (T, J )
Other problems
The common shock model
Copulas
Notes and references
Exercises
Risk Theory
The collective risk model
Introduction
The mean and variance of S
Generating functions
Exact distribution of S
Choosing a frequency distribution
Choosing a severity distribution
Handling the point mass at 0
Counting claims of a particular type
The sum of two compound Poisson distributions
Deductibles and other modifications
A recursion formula for S
Notes and references
Exercises
Risk Assessment
Introduction
Utility theory
Convex and concave functions: Jensen's inequality
A general comparison method
Risk measures for capital adequacy
Notes and references
Exercises
An introduction to stochastic processes
Introduction
Markov chains
Martingales
Finite-state Markov chains
Notes and references
Exercises
Poisson processes
Introduction
Definition of a Poisson process
Waiting times
Some properties of a Poisson process
Non homogeneous Poisson processes
Compound Poisson processes
Notes and references
Exercises
Ruin models
Introduction
A functional equation approach
The martingale approach to ruin theory
Distribution of the deficit at ruin
Recursion formulas
The compound Poisson surplus process
The maximal aggregate loss
Notes and references
Exercises
Credibility theory
Introductory material
Conditional expectation and variance
General framework for Bayesian credibility
Classical examples
Approximations
Conditions for exactness
Estimation
Notes and references
Exercises
Multi-state models
Introduction
The discrete-time model
The continuous-time model
Notes and references
Exercises
review of probability theory
Introduction
Sample spaces and probability measures
Conditioning and independence
Random variables
Distributions
Expectations and moments
Expectations in terms of the distribution function
The normal distribution
Joint distributions
Conditioning and independence for random variables
Convolution
Moment generating functions
Probability generating functions
Mixtures
Answers to exercises
References
Index
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