Bonus-Mains Systems in Automobile Insurance

Bonus-Mains systems are widely used in automobile insurance. In this paper some ideas of how to make BMS more effective in automobile insurance are discussed. At first part, we introduce the optimal BMS that have have been presented by Lemaire （1995）. At second part, some faults of optimal BMS are shown and absolutely fair BMS and relatively fair BMS are presented. At last part, we show how to consider claim size in optimal BMS when supposed that claim size of a policyholder is all exponential variable with parameter θ and in the portfolio θ varies from one policyholder to another and is a Gamma distribution.