Study Of The Auto-insurance Models And Bonus-Malus Systems

It is worldwide accepted that any insurer who aims to posses and maintain certain amountof automobile insurance market would use BMS(Bonus-Malus System) or so called NCD(No-Claim Discount) system. In this system, the insurance company will adjust its renew premiumaccording to the policyholder's claims of the previous years in order to make the policyholdera?ord the fair premium.The main contents in this paper can be summarized as follows:1. Firstly, in the first section, we introduce the origin of auto-insurance, auto-insurancedevelopment of abroad and home. Secondly, the organization of this paper is given.2. In the second section, for the Poisson-Gamma translation approximation distribution,first, we give the design of the BMS based on a posteriori claim frequency component. Second,the BMS designed to take severity into consideration are obtained. Finally, we present the BMSwith a frequency and a severity component based on the posteriori criteria.3. In the third section, firstly, desirable probability distribution of BMS is obtained usinginformation entropy. Secondly, a new model which takes into account the number of bodilyinjury claims in an insurance portfolio is developed. Then the di?erence between the stationaryprobability distribution of BMS and desirable probability distribution is presented byχ2 valueand redundancy respectively, which can be as a new tool of evaluation of BMS.4.In the fourth section, we consider four multi-risk Poisson distributions, and present BMSusing exponential loss function with these four distributions respectively.5.In the fifth section, we consider pricing no claims discount systems with relative premiumdiscount and di?erent levels. Furthermore, we give the optimal threshold values of the insuredfor two insurance companies of China which use NCD systems.