• 作者:  Christel Geiss
• 页数: 101页
• 语种： 英语
  

Insurance Mathematics is sometimes divided into life insurance, health in-surance and non-life insurance. Life insurance includes for instance life insurance contracts and pensions where long terms are covered. Non-life insurance comprises insurances against re, water damage, earthquake, industrial catastrophes or car insurance, for example. Non-life insurances cover in general a year or other xed time periods. Health insurance is special because it is dierently organized in each country.
The course material is based on the textbook Non-Life Insurance Mathematics by Thomas Mikosch



目录：
1 Introduction 5
1.1 Some facts about probability . . . . . . . . . . . . . . . . . . 6
2 Claim number process models 9
2.1 The homogeneous Poisson process . . . . . . . . . . . . . . . . 9
2.2 The renewal process . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 The inhomogeneous Poisson process... . . . . . . . . . . . . . . 19
3 The total claim amount process S(t) 23
3.1 The Cramer-Lundberg-model . . . . . . . . . . . . . . . . . . 23
3.2 The renewal model . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Properties of S(t) . . . . . . . . . . . . . . . . . . . . . . . . . 24
4 Premium calculation principles 29
4.1 Used principles . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5 Claim size distributions 31
5.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.3 The QQ-plot . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
6 Modern premium calculation principles 35
6.1 The exponential principle . . . . . . . . . . . . . . . . . . . . 35
6.2 The quantile principle . . . . . . . . . . . . . . . . . . . . . . 35
6.3 The Esscher principle . . . . . . . . . . . . . . . . . . . . . . . 35
7 The distribution of S(t) 37
7.2 Mixture distributions . . . . . . . . . . . . . . . . . . . . . . . 38
7.3 Applications in insurance . . . . . . . . . . . . . . . . . . . . . 40
7.4 The Panjer recursion . . . . . . . . . . . . . . . . . . . . . . . 42

7.5 Approximation of FS(t) . . . . . . . . . . . . . . . . . . . . . . 45
7.6 Monte Carlo approximations of FS(t) . . . . . . . . . . . . . . 46
8 Reinsurance treaties 49
9 Probability of ruin 51
9.1 The risk process . . . . . . . . . . . . . . . . . . . . . . . . . . 51
9.2 Bounds for the ruin probability . . . . . . . . . . . . . . . . . 55
9.3 An asymptotics for the ruin probability . . . . . . . . . . . . . 67
10 Problems 81
A The Lebesgue-Stieltjes integral 95
A.1 The Riemann-Stieltjes integral . . . . . . . . . . . . . . . . . . 95
A.2 The Lebesgue-Stieltjes integral . . . . . . . . . . . . . . . . . . 96