The Generalization And Application Of Bonus-Malus System

Bonus-Malus System is an important research project in non-life actuary. In essence. The system is that the insurer asks more premium to the policy holders who had one or more claims in last year, and gives discount to the policy holders who had no claims in last year.And we try our best to get an optimal system in a sense. From insurance practice, we know that BMS has important theoretical and practical sense to insurance on motor vehicles. In this paper, we mainly discuss the BMS about multi-risk insurance portfolio. There are four parts in this paper.In the first part of the paper,we introduce the background and significance of BMS and its advantages and disadvantages, and we also review the literature on BMS.In the second part,we research the mathematical modelling of BMS.In most companies, the importance of the auto-insurance prompted their actuaries to look for different tariff systems that distribute the exact weight of each risk among portofolios.In most situations, they use quadratic loss function but it must cause high penalty,and this will influnce the market competition of the policy product. In order to avoid the problem.In the paper, we use an entropy loss function.In the third part,the application of the multi-risk Poisson distribution in BMS are discussed. In the classical Bonus-Malus System, most research and discussion are about sole risk responsibility situation. But the design of BMS of most multiple risk responsibility situation such as automobile comprehensive insurance have more attraction. So we consider the BMS about multi-risk insurance portfolio. We use multi-risk Poisson-lognormal distribution and multi-risk Poisson-Inverse Guassian distribution.At the end of the paper, the BMS are used in the life insurance.