After a short introduction into credibility with some basics (e.g. the two urn-model) and some general results (e.g. the normal equations), the most important credibility-models such as the Bühl¬mann-Straub model, the Bühlmann-Straub model with a priori differentiation, the hierarchical credibility model, the multidimensional credibility model and the credibility regression model will be treated. For each of these models the formulae of the credibility estimators and their quadratic loss will be presented.
However the main focus of this workshop will be on practical examples. On the basis of worked out examples, most of them based on real data from practice, it is shown how credibility can be applied in practice.
These applications encompass:
- Bühlmann Straub applied to estimating claim frequencies, claim severities, burning costs, or the Pareto-Parameter for xs-reinsurance;
- Bühlmann Straub with a priori differentiation applied to experience rating for fleets of cars; adjustment of a given tariff based on new observed data;
- individual adjustment of the level of mortality and invalidity curves;
- an example of hierarchical credibility of order 2;
- multidimensional credibility applied to pricing, adjusting mortality curves, claims reserving;
- an example of simple linear regression.
To give the participants as much time as possible for hands-on exercises in a two-day seminar, many theorems will be presented without proof. But as the seminar is based on the following book, all results and proofs can be found there:
Bühlmann H. and Gisler A. (2005), A Course in Credibility Theory and its Applications, Springer Verlag
