# Insurance Risk and Ruin

###### David C. M. Dickson
Publisher:
Cambridge University Press
Publication Date:
2005
Number of Pages:
229
Format:
Hardcover
Series:
International Series on Actuarial Science
Price:
60.00
ISBN:
0-521-84640-4
Category:
Textbook
We do not plan to review this book.

Preface page xi

1 Probability distributions and insurance applications 1

1.1 Introduction 1

1.2 Important discrete distributions 2

1.3 Important continuous distributions 5

1.4 Mixed distributions 9

1.5 Insurance applications 11

1.6 Sums of random variables 18

1.7 Notes and references 23

1.8 Exercises 24

2 Utility theory 27

2.1 Introduction 27

2.2 Utility functions 27

2.3 The expected utility criterion 28

2.4 Jensen’s inequality 29

2.5 Types of utility function 31

2.6 Notes and references 36

2.7 Exercises 36

3 Principles of premium calculation 38

3.1 Introduction 38

3.2 Properties of premium principles 38

3.3 Examples of premium principles 39

3.4 Notes and references 50

3.5 Exercises 50

4 The collective risk model 52

4.1 Introduction 52

4.2 The model 53

4.3 The compound Poisson distribution 56

4.4 The effect of reinsurance 59

4.5 Recursive calculation of aggregate claims distributions 64

4.6 Extensions of the Panjer recursion formula 72

4.7 The application of recursion formulae 79

4.8 Approximate calculation of aggregate claims distributions 83

4.9 Notes and references 89

4.10 Exercises 89

5 The individual risk model 93

5.1 Introduction 93

5.2 The model 93

5.3 De Pril’s recursion formula 94

5.4 Kornya’s method 97

5.5 Compound Poisson approximation 101

5.6 Numerical illustration 105

5.7 Notes and references 108

5.8 Exercises 108

6 Introduction to ruin theory 112

6.1 Introduction 112

6.2 A discrete time risk model 113

6.3 The probability of ultimate ruin 114

6.4 The probability of ruin in finite time 118

6.5 Lundberg’s inequality 120

6.6 Notes and references 123

6.7 Exercises 123

7 Classical ruin theory 125

7.1 Introduction 125

7.2 The classical risk process 125

7.3 Poisson and compound Poisson processes 127

7.4 Definitions of ruin probability 129

7.6 Lundberg’s inequality 133

7.7 Survival probability 135

7.8 The Laplace transform of φ 138

7.9 Recursive calculation 142

7.10 Approximate calculation of ruin probabilities 151

7.11 Notes and references 153

7.12 Exercises 154

8.1 Introduction 157

8.2 A barrier problem 157

8.3 The severity of ruin 158

8.4 The maximum severity of ruin 163

8.5 The surplus prior to ruin 165

8.6 The time of ruin 172

8.7 Dividends 180

8.8 Notes and references 186

8.9 Exercises 187

9 Reinsurance 190

9.1 Introduction 190

9.2 Application of utility theory 190

9.3 Reinsurance and ruin 194

9.4 Notes and references 205

9.5 Exercises 206

References 208

Solution to exercises 211

Index