Lectures on Risk Theory

1. Front Matter

   Pages i-x

   PDF

2. Introduction

   • Klaus D. Schmidt

   Pages 1-4

3. The Claim Arrival Process

   • Klaus D. Schmidt

   Pages 5-16

4. The Claim Number Process

   • Klaus D. Schmidt

   Pages 17-42

5. The Claim Number Process as a Markov Process

   • Klaus D. Schmidt

   Pages 43-84

6. The Mixed Claim Number Process

   • Klaus D. Schmidt

   Pages 85-102

7. The Aggregate Claims Process

   • Klaus D. Schmidt

   Pages 103-126

8. The Risk Process in Reinsurance

   • Klaus D. Schmidt

   Pages 127-154

9. The Reserve Process and the Ruin Problem

   • Klaus D. Schmidt

   Pages 155-170

10. Back Matter

    Pages 171-202

    PDF

Twenty-five years ago, Hans Blihlmann published his famous monograph Mathe­ matical Methods in Risk Theory in the series Grundlehren der Mathematischen Wis8enschaften and thus established nonlife actuarial mathematics as a recognized subject of probability theory and statistics with a glance towards economics. This book was my guide to the subject when I gave my first course on nonlife actuarial mathematics in Summer 1988, but at the same time I tried to incorporate into my lectures parts of the rapidly growing literature in this area which to a large extent was inspired by Blihlmann's book. The present book is entirely devoted to a single topic of risk theory: Its subject is the development in time of a fixed portfolio of risks. The book thus concentrates on the claim number process and its relatives, the claim arrival process, the aggregate claims process, the risk process, and the reserve process. Particular emphasis is laid on characterizations of various classes of claim number processes, which provide alternative criteria for model selection, and on their relation to the trinity of the binomial, Poisson, and negativebinomial distributions. Special attention is also paid to the mixed Poisson process, which is a useful model in many applications, to the problems of thinning, decomposition, and superposition of risk processe8, which are important with regard to reinsurance, and to the role of martingales, which occur in a natural way in canonical situations.

• Claim Arrival Process
• Claim Number Process
• Erlang C
• Martingal
• Mixed Claim Number Process
• development
• mathematics
• model
• probability
• probability theory
• quality
• risk
• statistics

• Techn. Universität Dresden, Germany

  Klaus D. Schmidt

Policies and ethics