Insurance Risk And Ruin保险事故与毁灭理论
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作者： David C. M. Dickson 著
出 版 社：
出版时间： 2005-1-1字数：版次： 1页数： 229印刷时间： 2005/01/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780521846400包装： 精装内容简介
Based on the author's experience of teaching final-year actuarial students in Britain and Australia, and suitable for a first course in insurance risk theory, this book focuses on the two major areas of risk theory - aggregate claims distributions and ruin theory. For aggregate claims distributions, detailed descriptions are given of recursive techniques that can be used in the individual and collective risk models. For the collective model, different classes of counting distribution are discussed, and recursion schemes for probability functions and moments presented. For the individual model, the three most commonly applied techniques are discussed and illustrated. Care has been taken to make the book accessible to readers who have a solid understanding of the basic tools of probability theory. Numerous worked examples are included in the text and each chapter concludes with exercises, which have answers in the book and full solutions available for instructors from www.cambridge.org.
The book is ideal for a first course in insurance risk theory. It focuses on major areas in this subject - aggregate claims distributions, ruin theory, utility theory, premium calculation principles and reinsurance problems. Numerous worked examples are included and each chapter has exercises for which outline solutions are provided.
目录
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
