The Bonus-Malus System And Ratemaking In Automobile Insurance

Actuarial science applies mathematical methods in insurance and is a science between applied mathematics and insurance. Bonus-malus system of automobile insurance is an important topic in actuarial science.Markov chain, Statistical theory and Optimization method are used to study bonus-malus 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 estimated by maximum likelihood in the two distributions. Finally, we gave a example and analyzed the results.2. We study optimal bonus-malus system in which claim frequency is used as posterior factor. Two optimal four level BMSs with present Chinese BMS's transfer rule are obtained under two objects, minimize insurer's expected loss .We also study path-dependent BMS with linear BM coefficients. If transfer rule is related to more than one past periods' claim record, we can get a new rule by adding a subscript to each BM level. The new rule is a Markov chain, An optimal BMS is obtained to minimum insurer's expected loss under linear restrict.3. Besides claim number, claim amount is used in BMS. In the BMS, in the BMS considering both claim frequency and claim severity, expected value principle and expected-variance principle are used to build optimal BMS.4. 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.5. We do practical research on BMS, we compare and comment on the Bonus-Malus antomobile insurance systems of five Chinese automobile companies in detail, at the same time point out the lacks.