Authors: Hans Buhlmann, Alois Gisler, Hans Ba1/4hlmann
ISBN-13: 9783540257530, ISBN-10: 3540257535
Format: Paperback
Publisher: Springer-Verlag New York, LLC
Date Published: September 2005
Edition: (Non-applicable)
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
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 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. 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.
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.
1 | Introduction | 1 |
2 | The Bayes premium | 15 |
3 | Credibility estimators | 55 |
4 | The Buhlmann-Straub model | 77 |
5 | Treatment of large claims in credibility | 125 |
6 | Hierarchical credibility | 143 |
7 | Multidimensional credibility | 167 |
8 | Credibility in the regression case | 199 |
9 | Evolutionary credibility models and recursive calculation | 219 |
10 | Multidimensional evolutionary models and recursive calculation | 251 |
App. A | Basic elements from probability theory | 275 |
App. B | The Hilbert space L[superscript 2] | 283 |
App. C | Solutions to the exercises | 287 |