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, auto insurance business premium income usually occupies 80% of the company's total premium income. Therefore, pricing the auto insurance rates scientifically and rationally is essential.The Bonus-Malus system (BMS) is widely used in automobile insurance.It is based mainly on the driver's records of historical claims to determine their renewal premium. In China, many insurance companies have separately developed its own BMS or No Claim Discount system(NCD system).In this paper,we will use Markov chain knowledge and mathematical statistical theory to study auto insurance system, with a focus on the design and improvement of BMS.The primary research content and results are obtained as follows:1. BMS will be researched by Markov chain.I will draw the conclusion that every BMS has stationary distribution.2. Besides claim number, claim amount is used in BMS.A application model of BMS will be established, considering both claim number and claim amount. And the application model will be analysied, including the Transfer Matrix, StabilityDistribution, the determination of the premium grade, and so on. Finally, the Empirical Analysis will be done.3. The initial deductible model has poor obvious defects.The establishment of a new model of flexible deductible can compensate for the initial model' deficiencies. Based on the the limited mathematical expectation, the density function and other mathematical tools,we analyze the impact of the use of different types of deductible and compensation limit on the pure premiums. It has great significance for the insurance and actuarial staff to design more rational and more fair insurance types.4.Finally,I will expound some issues which are worthy of being further researched.