Designing an Optimal Bonus-Malus System based upon both Frequency and Severity of accidents

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Designing an Optimal Bonus-Malus System based upon both Frequency and Severity of accidents

Abstract

The majority of optimal Bonus-Malus Systems that are presented in the actuarial literatures assign to each policyholder a premium based on the number of policyholder’s accidents. In this way a policyholder who had an accident with a small size of loss is penalized unfairly in the same way with a policyholder who had an accident with a big size of loss. This thesis designs an optimal Bonus-Malus System with both a frequency and severity components. The model includes the important priori information for each policyholder. For this purpose we consider the generalized additive models for location, scale and shape in order to use all available information in the estimation of the claim frequency distribution. We proposed a generalized Bonus-Malus System that takes into consideration simultaneously the individual’s characteristics, the number of policyholder’s accidents and the level of severity for each accident. This thesis considers k-inflated finite mixture negative binomial models for frequency component for the first time in the literatures of Bonus-Malus Systems and results show that this model is the best model for frequency of claims.

Keywords: Bonus-Malus Systems; frequency and severity of accident; k-inflated finite mixture models.