Lectures on Insurance Models

Insurance has become a necessary aspect of modern society. The mathematical basis of insurance modelling is best expressed in terms of continuous time stochastic processes.

This introductory text on actuarial risk theory deals with the Cramer-Lundberg model and the renewal risk model. Their basic structure and properties including the renewal theorems, as well as the corresponding ruin problems are studied. As heavy tailed distributions have become increasingly relevant, there is a detailed discussion on such distributions. The Lundberg risk process with investment in risky asset is also considered.

The book will be useful to practitioners in the field and to graduate students interested in this important branch of applied probability.

Contents

1. Introduction
2. Poisson model
3. Renewal model
4. Claim size distributions
5. Ruin Problems
6. Lundberg risk process with investment
Appendix 1. Basic notions
Appendix 2. On the central limit problem
Appendix 3. Martingales
Appendix 4. Brownian motion and Itô integrals
Bibliography
Index