Analysis Of The Bonus-Malus System In Automobile Insurance

The automobile insurance is important in modern insurance industry. In most of the property insurance companies in our country, car insurance business premium income usually occupies 80% of the total benefit income. Therefore, it is important to pricing the automobile insurance scientifically and reasonably. The Bonus-Malus system (BMS) is extensively applied in automobile insurance. Its main idea is to determine the premium according to the driver's historic claim records. In China, many insurance companies have their own No Claim system (NCD system), too.This paper will first introduce BMS, then study BMS by Markov chain in stochastic process and INAR(1) model in time series.In chapter 1, we will see the advantage of BMS and the situation of BMS research. In chapter 2, BMS will be researched by Markov chain. I will draw the conclusion that every BMS has stationary distribution. In chapter 3,I will try to study BMS from another angle: using time series method to pricing the automobile insurance. I will fit the claim frequency by INAR(l) model, then predict the risk of the insurer by the one-order forecast of the model. Base on it, I can calculate the premium of the insurer. Some recommendations about the automobile insurance business will be given in chapter 4. At last, in chapter 5, I will expound some issues which are worthy of being further researched.The innovations of this paper are in chapter 2 and chapter 3. Professor Chen Shixue has studied No Claim Discount system by Markov chain, I will go ahead to modeling the Bonus-Malus system and make stability analysis of BMS in chapter 2. Scholars always assume that the claim frequency follow some distribution, such as Poisson. But in chapter 3 of this paper, I study the claim frequency by time series theory.