The topic of credibility theory has been for many years -- and still is -- one of our major interests. This interest has led us not only to many publications, but also has been the motivation for teaching many courses on this topic over more than 20 years. These courses have undergone considerable changes over time. What we present here, A Course in Credibility Theory and its Applications, is the ?nal product of this evolution. Credibility theory can be seen as the basic paradigm underlying the pricing of insurance products. It resides on the two fundamental concepts individual risk and collective and solves in a rigorous way the problem of how to analyse the information obtained from these sources to arrive at the insurance premium. The expression credibility was originally coined for the weight given to the experience from the individual risk. Credibility theory as a mathematical discipline borrows its methods from 2 many ?elds of mathematics, e. g. Bayesian statistics, L Hilbert space te- niques, least squares, and state space modelling to mention only the most important ones. However, credibility theory remains a lifeless topic if it is not linked closely with its applications. Only through these applications has cr- ibility won its status in insurance thinking. The present book aims to convey this dual aspect of credibility and to transmit the ?avour of the insurance applications also to those readers who are not directly involved in insurance activities.
From the Back Cover The book is aimed at teachers and students as well as practising experts in the financial area, in particular at actuaries in the field of property-casualty insurance, life insurance, reinsurance and insurance supervision. Persons working in the wider world of finance will also find many relevant ideas and examples even though credibility methods have not yet been widely applied here. The text combines scientific rigour with direct practical applicability. It is based on courses given by the two authors at ETH Zürich. These courses have undergone considerable changes over time. A Course in Credibility Theory and its Applications is the final product of this evolution. It covers the subject of Credibility Theory extensively and includes most aspects of this topic from the simplest case to the most general dynamic model. The first four chapters contain plenty of material for a first course on Credibility. The whole text is intended as a full one year course at intermediate to advanced level. Credibility is a lifeless topic if it is not linked closely to practical applications. The book therefore treats explicitly the tasks which the actuary encounters in his daily work such as estimation of loss ratios, claim frequencies and claim sizes. The models are worked out in detail (including the estimation of structural parameters) so that they can immediately be applied in practice. Most exercises are based on real insurance data and real situations from practice and many of them have the characteristics of a case study. The extension to practical problems arising from the general area of finance is often quite straightforward. This book deserves a place on the bookshelf of every actuary and mathematician who works, teaches or does research in the area of insurance and finance.