The Bonus-Malus System And Ratemaking In Automobile Insurance

Actuarial mathematics is a marginal science between applied mathematics and insurance study field. Bonus-malus system (BMS in short) in automobile insurance is an experiential rating system, which extensively used in automobile insurance. It is used to determining the premiums according to the driver's historic claim records. Bonus-malus system is becaming a more important theme in Actuarial mathematics as it associates with ratemaking.Markov chain, Statistical theory and Optimization method are used to study bonus-malu- s systems, mainly focusing on revising and designing of the bonus-malus system. the primary research content and results are obtained as followes:1. Based on the characteristic that the claim number which reported is less than the practical accident number in a portfolio of insurance policyholder, the paper presented a new class of claim distribution to fit the claims numbers on homogeneous policyholders. Parameters are estimated by maximum likelihood in the two distributions. Finally, we gave a example and analyzed the results.2. We presented a method to compute the premium coefficient for each level of the scale when the claim frequency distribution is assumed to conform negative binomial distribution or the nonparametric mixed poisson distribution, the theoretic models of bonus-malus systems are applied to the practical bonus-malus systems model with limited scale by this way.3. We constructed an applied BMS involving claim amount and responsibility to abate unfair in the BMS in which claim number is considered as only factor.4. Considering the policyholder'prior information in the modle with a deductible varying according to the level occupied in the scales, we revisited the original method to computer the deductible. In the modle, we also considered the financial balanced for the insurance agent. So, the deductible is further scientific and reasonable.5. We constructed a bonus-malus systems based on the type of claims. The claims are divided into material damage and bodily injury, expected value principle is used to compute the bonus-malus systems'premium.