Based on the author's experience of teaching final-year actuarial students in Britain and Australia, and suitable for a first course in insurance risk theory, this book focuses on the two major areas of risk theory - aggregate claims distributions and ruin theory. For aggregate claims distributions, detailed descriptions are given of recursive techniques that can be used in the individual and collective risk models. For the collective model, different classes of counting distribution are discussed, and recursion schemes for probability functions and moments presented. For the individual model, the three most commonly applied techniques are discussed and illustrated. Care has been taken to make the book accessible to readers who have a solid understanding of the basic tools of probability theory. Numerous worked examples are included in the text and each chapter concludes with exercises, which have answers in the book and full solutions available for instructors from www.cambridge.org/9780521846400.

'… requires some mathematical maturity but provides a good insight into how probability distributions tie in with insurance applications.'

Source: Journal of Applied Statistics

'… a nice introduction to some basic aspects of risk theory, with special emphasis on utility theory, recursive methods and ruin theory … What I appreciate most is the way in which the author explains the different topics dealt with in this book.'

Source: Publication of the International Statistical Institute

'This book is well written. It is also well organized. … For practitioners, it may be of interesting reference, and a way to have a good overview of some recent developments in ruin theory.'

Source: ASTIN Bulletin

'… a carefully and well written monograph on insurance risk and ruin, providing the higher-year student with the basic tools and concepts in these areas. Lecturers will find it a useful textbook for a corresponding course to teach in an actuarial program.'

Source: Zentralblatt MATH

'All in all, this is a nice textbook, especially for students with a limited background in probability. In particular, it should be useful for students studying for the professional examination … I am not aware of any book on the same level in which ruin theory is treated so deeply.'

Source: Journal of the American Statistical Association

'… provides an accessible treatment of some of the most fundamental concepts in the classical development of insurance portfolio modelling, admirably treading the tightrope between rigorous detail and intuitive argument … an excellent undergraduate treatment of an important and often daunting subject and will make a more than useful addition to the shelves of both actuarial educators and students alike.'

Source: Gazette of the Australian Maths Society

'… this is a book which can well be recommended to students interested in risk and ruin and wanting a good readable account that goes beyond the syllabus of the professional examinations.'

Source: South African Actuarial Journal

'… a good accessible treatment of some of the most fundamental concepts cleverly walking the fine line between too much rigorous detail and not enough. It is a good book for student reference in university libraries.'

Source: Mathematics Today

'A clear, concise and well written textbook on two daunting actuarial areas … The exposition is so clear that it feels like [the author is] talking to you … This is an excellent book equally suitable for self-study and classroom instruction. It is highly recommended as supplementary reading for students studying for their professional exams and as an overview of the latest developments in risk models, ruin theory and reinsurance for practitioners.'

Seow Fan Chong Source: Annals of Actuarial Science

'this well written and well organised book provides a good insight into how probability theory ties with insurance applications.'

Source: Zentralblatt MATH