A Comparison of Several Bonus Malus Systems

The paper deals with the automobile third party liability insurance and several bonus malus system are compared in it on the basis of Loimaranta efficiency. Very important task for actuary is creating rating system that will fairly distributed the burden of claims among policyholders. For these purposes, most insurance companies use generalized linear models, especially Poisson regression. Thanks to these models the a priori tariff structure is created. But some heterogeneity still remains in this tariff structure. Therefore, insurance companies use the bonus malus system that rewards good drivers and penalizes bad drivers. In this paper the bonus malus system for sample of data is created and bayesian relativities are computed. Then this bonus malus system is compared with several bonus malus systems from Czech Republic. The elasticity of these bonus malus systems is examined and then Loimaranta efficiency is used as main tool for comparison these systems.