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Large claims in credibility. (English) Zbl 0738.62097
The present paper which has been presented to the International ASTIN Colloquium in 1991 deals with the problem of “large” and - as the author calls it - “much larger” claims in experience rating. First, the author gives a survey of some basic models in credibility theory. Then he develops procedures for data sets with outliers (“large claims”) in the classical model of credibility theory by using techniques from the theory of robust estimation (\(M\)- and \(L\)-estimators). Subsequently, this approach is extended to the regression model and applied to the so-called Bühlmann-Straub model.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
62F35 Robustness and adaptive procedures (parametric inference)
91B30 Risk theory, insurance (MSC2010)
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