Credibility rating in a multiplicative tariff

Credibility theory is a useful tool for the rating of multi-level factors (MLFs), i.e. categorical rating factors with a large number of levels that can not be grouped in a natural way. In practice we often have a number of ordinary rating factors besides the MLF. We extend the Bühlmann-Straub estimator to the situation with both an MLF and ordinary rating factors in a multiplicative tariff. An application to private motor car insurance is presented.

Keywords: Rating, credibility theory, Bühlmann-Straub, Jewell’s theorem, multi-level factor, multiplicative model.