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.

Hans Bühlmann

Hans Bühlmann is professor emeritus of ETH Zürich, where he taught mathematics for more than thirty years. He has held visiting appointments at UC Berkeley, University of Michigan, UL Bruxelles, University of Tokyo, University of Manitoba, Università La Sapienza in Rome, Scuola Normale Superiore Pisa. His interest in actuarial science dates back to his first employment after his doctorate, when he worked in the insurance industry. His book "Mathematical Methods in Risk Theory" (Springer Grundlehren) is a classic in the actuarial literature. www.math.ethz.ch/~hbuhl

Alois Gisler

Alois Gisler is chief actuary at Winterthur Insurance Company and professor at ETH Zürich, where he teaches non-life insurance mathematics and credibility. He wrote his doctoral thesis with Hans Bühlmann at ETH, and since then has worked for more than twenty years in the insurance industry. While a full time practising actuary, he has always kept in close contact with actuarial science: he was co-editor of the ASTIN-Bulletin for 10 years and has published many articles, mainly in credibility theory.

www.math.ethz.ch/~gisler

This book is ideal for practicing experts in particular actuaries in the field of property-casualty insurance, life insurance, reinsurance and insurance supervision, as well as teachers and students. It provides an exploration of Credibility Theory, covering most aspects of this topic from the simplest case to the most detailed dynamic model. The book closely examines the tasks an actuary encounters daily: estimation of loss ratios, claim frequencies and claim sizes.

The Bayes Premium.- Credibility Estimators.- The Bühlmann-Straub Model.- Treatment of Large Claims in Credibility.- Hierarchical Credibility.- Multidimensional Credibility.- Credibility in the Regression Case.- Evolutionary Credibility Models and Recursive Calculation.- Multidimensional Evolutionary Models and Recursive Calculation.