Designing an optimal bonus-malus system using the number of reported claims, steady-state distribution, and mixture claim size distribution
by Amir T. Payandeh Najafabadi; Mansoureh Sakizadeh
International Journal of Industrial and Systems Engineering (IJISE), Vol. 32, No. 3, 2019

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.

Online publication date: Wed, 24-Jul-2019

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