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. There is a detailed discussion of heavy tailed distributions, which have become increasingly relevant. The Lundberg risk process with investment in risky asset is also considered.

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