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Practical actuarial credibility models. (English) Zbl 0905.62101

Amsterdam: Univ. of Amsterdam, Institute of Actuarial Science and Econometrics. x, 157 p. (1996).
The so-called credibility model of risk theory gives a mathematical framework for practical methods like experience rating and estimating IBNR (incurred but not reported) claims. Such models have been developed since the beginning of the century, but only in recent decades a sound mathematical framework for the different approaches has been derived. Among the best known procedures are regression techniques, analysis of variance, and Bayes methods.
In the present brochure, the authors present a collection of methods which, to their impression, are particularly important and understandable to the practical actuary and the students of actuarial mathematics. So only a short chapter of 12 pages is dedicated to the Bayes approach. Other well-known models, like the Bühlmann-Straub model, Jewell’s hierarchical model, and the Hachemeister regression model are explained extensively. Also the application of the De Vylder model to the IBNR problem is discussed in detail. There are only few numerical examples, but to each chapter a set of problems is attached.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
91B30 Risk theory, insurance (MSC2010)
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