A Course in Credibility Theory and Its Applications

ISBN-13: 9783540257530 / Angielski / Miękka / 2005 / 338 str.

Hans B]hlmann; Alois Gisler; Hans Buhlmann

Opis

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.

Recenzje

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)

Spis treści

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.

O autorze

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

Blurb

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.