| Automobile insurance is an important part of modern insurances. Whether in western countries with developed insurance or in our country with relatively developing insurance, automobile insurance plays an important role in the whole wealth insurance .Good management of automobile insurance will benefit in the company's commercial profit.Almost all insurance countries in the world are using Bonus-Malus System (BMS in short) in automobile insurance. In this system, the insurance company will adjust its renew premium according to the policy-holder's claims of the previous years. The general principle is like this: the more severity there is in the previous insurance year, the higher the renew premium will be in the following year. On the contrary, if there is no claim in the previous insurance year, the insurance company would reduce the policy-holder's renew premium. It is no doubt that one of the main aims of the adjustment of renew premium is to make the policy-holder afford the fair premium, which means that those who are in high risk should pay more insurance fee. However, experiments show that the systems that the insurance companies including many insurance companies in China implement could not reach the aim. So the optimal BMS came into being.Up to now, the optimal BMS in the international actuarial literature only consider the frequency of the claims in a year and ignore the amount of the claim, which means the punishment for small and large claims are treated equally. Based on Meng shengwang and Yuanwei's research under square loss function , this research sets up several Bonus and Malus Systems under a symmetric entropy loss function L(λ,δ) =λ/δ+δ/λ-2 by considering the claim frequency and by considering both the claim frequency and claim amount. The Bonus and Malus System under a symmetric entropy loss function L(λ,δ) =λ/δ+δ/λ-2 is also compared with the Bonus and Malus System under square loss function. The result has certain theoretical significance internationally besides the practical significance domestically it has. |
