A Course in Credibility Theory and its Applications

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.

Content:

Introduction.- The Bayes Premium.- Credibility Estimators.- The Bühlmann-Straub Model.- Treatment of Large Claims in Credibility.- Hierarchical Credibility. Multidimensional Credibility.- Credibility in the Regression Model.- Evolutionary Credibility Models and Recursive Calculation Methods (Kalman-Filter).- Multidimensional Evolutionary Credibility Models and Recursive Calculation Methods (Kalman-Filter).- Bibliography.- Index.

From the reviews:

"The book is aimed at teachers and students as well as practicing experts in the financial area ... . 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 book covers the subject of Credibility Theory extensively and includes most aspects of this topic from the simplest case to the most general dynamic model." (Zeitschrift für die gesamte Versicherungswissenschaft, Issue 2, 2006)

"The authors ... have done an excellent job while explaining the basic concept and at the same time elaborating on the practical problems actuaries encounter. ... The book is aimed at teachers, students and practising experts, especially actuaries working in property-casualty insurance. ... The book has relevant practical examples and exercises which practitioners might find useful. It may be useful for students/non-actuaries who do not have a statistical background ... ." (Gautam Kakar, Annals of Actuarial Science, Vol. 2 (2), 2007)