A Bonus-Malus system with more competitive rates by using the Esscher Principle

Abstract

The main purpose of the Bonus-Malus Systems is to better the individual risk, so that, policyholders will pay, in the long run, a premium corresponding to their own claim frequency. Nevertheless, in all Bonus-Malus system some people are unfairly penalized, since they pa more than their pure premium. We present a model, based on a suggestion of Lemaire (1979, pp. 278-281) which decreases these overcharges by minimizing the expectation of the Esscher loss function, obviously under the condition of financial balance of the system.