This book is designed for final-year university students taking a first course in insurance risk theory. Like many textbooks, it has its origins in lectures delivered in university courses, in this case at Heriot-Watt University, Edinburgh, and at the University of Melbourne. My intention in writing this book is to provide an introduction to the classical topics in risk theory, especially aggregate claims distributions and ruin theory.

The prerequisite knowledge for this book is probability theory at a level such as that in Grimmett and Welsh (1986). In particular, readers should be familiar with the basic concepts of distribution theory and be comfortable in the use of tools such as generating functions. Much of Chapter 1 reviews distributions and concepts with which the reader should be familiar. A basic knowledge of stochastic processes is helpful, but not essential, for Chapters 6 to 8. Throughout the text, care has been taken to use straightforward mathematical techniques to derive results.

Since the early 1980s, there has been much research in risk theory in computational methods, and recursive schemes in particular. Throughout the text, recursive methods are described and applied, but a full understanding of such methods can only be obtained by applying them. The reader should therefore by prepared to write some (short) computer programs to tackle some of the examples and exercises.

Many of these examples and exercises are drawn from materials I have used in teaching and examining, so the degree of difficulty is not uniform.