Research On The Current Bonus-Malus System Of The Auto Insurance In China

In pace with the rapid growth of China's auto ownership,auto insurance has been developing rapidly,and has become a leading insurance in the non-life insurance market of China.In order to promote the healthy development of China's auto insurance,China carried out the reform of vehicle insurance rate in 2016,and implemented the new auto insurance rate.As an important part of auto insurance's rate determination,the Bonus-Malus system(BMS)is worthy of further research.First of all,we analyze and evaluate the current BMS of auto insurance in China to find that the current BMS of the auto insurance determines the reward and punishment coefficient based on the number of claims of last year,without considering the premium grade of the insured in the last year,which makes the transfer rules are simple.In order to analyze its severity,the paper uses negative binomial distribution to fit the claim number distribution,and constructs a transfer probability matrix,and then obtains the steady-state probability distribution according to the Markoff property of the BMS,and then relative stationary average level,excess charge level and coefficient of variation are figured out based on the steady-state probability distribution to analyze the current BMS of our country.It shows that when the current BMS of the auto insurance is in a stable state,the degree of concentration of the insured in the minimum premium discount level is high,that is the punishment is mild and the severity is insufficient.Secondly,aiming at the existing problems of the current BMS of auto insurance,this paper attempts to build a BMS based on the aggregate claim amount.In order to make full use of the information of the claim numbers and the the claim amount,the paper constructs a piecewise function of the aggregate claim amount,and on this basis,the paper establish a BMS based on the aggregate amount of claims in which the insured person's reward and punishment coefficient in the next year is determined by the premium grade and the cumulative claim amount in the last year.Through analysis,the newly established BMS has Markov nature,that is to say there exists a steady state distribution.Then the zero adjustment Pareto distribution is used to fit the aggregate claim amount,and the transfer probability matrix of the BMS based on the aggregate claim amount is constructed to solve the steady-state probability distribution,and further calculate relative stationary average level,excess charge level and coefficient of variation.Compared with the current BMS of the auto insurance in China,the insured is evenly distributed in all premium grades when BMS is in a stable state,and the punishment is more severe.In the end,in view of the difficulties in implementing the BMS based on the aggregate claim amount,the countermeasures are proposed in four aspects: organization,platform,talents and funds,to guarantee the BMS based on the aggregate claim amount can be implemented successfully.The design of the BMS is solely based on the information of claim numbers and the amount of claim,but doesn't consider the posterior risk information such as accident liability and insurance fraud.With the gradual advance of China's auto insurance rate reform,taking full consideration of the posterior risk information of the insured and further refining the risk classification are bound to be the direction of the development of China's auto insurance and the direction for further research.