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DACID C.M.DICKSON， Centre for Actuarial Studies Department of Economics ,University of Melbourne
Preface
1 Probability distributions and insurance applications
1.1 Introduction
1.2 Important discrete distributions
1.3 Important continuous distributions
1.4 Mixed distributions
1.5 insurance applications
1.6 Sums of random variables
1.7 Notes and references
1.8 Exercises
2 Utility theory
2.1 Introduction
2.2 Utility functions
2.3 The expected utility criterion
2.4 Jensen's inequality
2.5 Types of utility function
2.6 Notes and references
2.7 Exercises
3 Principles of premium calculation
3.1 Introduction
3.2 Properties of premium principles
3.3 Examples of premium principles
3.4 Notes and references
3.5 Exercises
4 The collective risk model
4.1 Introduction
4.2 The model
4.3 The compound Poisson distribution
4.4 The effect of reinsurance
4.5 Recursive calculation of aggregate claims distributions
4.6 Extensions of the Panjer recursion formula
4.7 The application ofrecursion formulae
4.8 Approximate calculation of aggregate claims distributions
4.9 Notes and references
4.10 Exercises
5 The individual risk model
5.1 Introduction
5.2 The model
5.3 De Pril's recursion formula
5.4 Kornya's method
5.5 Compound Poisson approximation
5.6 Numerical illustration
5.7 Notes and references
5.8 Exercises
6 Introduction to ruin theory
6.1 Introduction
6.2 A discrete time risk model
6.3 The probability of ultimate ruin
6.4 The probability of ruin in finite time
6.5 Lundberg's inequality
6.6 Notes and references
6.7 Exercises
7 Classical ruin theory
7.1 Introduction
7.2 The classical risk process
7.3 Poisson and compound Poisson processes
7.4 Definitions of ruin probability
7.5 The adjustment coefficient
7.6 Lundberg's inequality
7.7 Survival probability
7.8 The Laplace transform of
7.9 Recursive calculation
7.10 Approximate calculation of ruin probabilities
7.11 Notes and references
7.12 Exercises
8 Advanced ruin theory
8.1 Introduction
8.2 A barrier problem
8.3 The severity of ruin
8.4 The maximum severity of ruin
8.5 The surplus prior to ruin
8.6 The time of ruin
8.7 Dividends
8.8 Notes and references
8.9 Exercises
9 Reinsurance
9.1 Introduction
9.2 Application of utility theory
9.3 Reinsurance and ruin
9.4 Notes and references
9.5 Exercises
References
Solution to exercises
Index
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