Abstract
This article, in a first step, considers two Bayes estimators for the relativity premium of a given bonus-malus system. It then develops a linear relativity premium that closes, in the sense of weighted mean square error loss, to such Bayes estimators. In a second step, it supposes that the claim size distribution for a given bonus-malus system can be formulated as a finite mixture distribution. It then evaluates the base premium under a Bayesian framework for such a finite mixture distribution. The Loimaranta efficiency of such a linear relativity premium, for several bonus-malus systems, has been compared with two Bayes and ordinary linear relativity premiums.
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