Research On The Bonus-Malus System Of The Automobile Insurance

The BMS(Bonus-Malus System)is a prize and punishment system, in motor vehicle insurance it is called to be no-claim bonus system and widely adopted system in the motor vehicle insurance: in the next insurance year, the policyholders who have some claim records will be punished for premium from the insurance company, while those who have no claim record will be rewarded. It's shown that the BMS is very necessary and means much in insurance practice. As to the necessity:The risk levels differ among different policyholders, that is to say, during the same term of insurance, it's impossible for the numbers of claims to be equal for different policyholders, which are called risk heterogeneity. At the same time, insurance companies take distinguishing premiums from policyholders with different risk levels.In this paper, we first introduce the background and the significance of this study, the necessity and the current status of studies on BMS and focus in our work is also stated in details in Chapter one. In Chapter two, we choose two better models, Negative-Binomial Distribution Model and the Ternary Distribution Model from some usual distribution models of the claims number, through superimposing, better fitting model which is more approximate to the real data is obtained. This new model will provide more useful information for insurance companies to develop more reasonable pricing diploma. Chapter three discusses a special claim case about the two drivers with almost the same basic information. If one driver claims once in the fifth year while the other driver claims once in the tenth year and both drivers has no claims in other years, their insurance costs will be of great differences. To deal with this case, we propose to apply time series method to the study of the claims number. Therefore, BMS is more popular with the two assureds who share similar information because the premium for them is almost the same. In Chapter four, the BMS is introduced a Korea company called SFMI which is the only insurance company who considers the size of an insurance claim in the world. We improved their BMS to make it more competitive in the market.