Design Of Bonus-Malus System In Automobile Insurance

The main idea for ratemaking in automobile third-party liability insurance is as below: first we divide the drivers into several homogeneous portfolios according to a priori rating variables for individual's characteristics (such as age, gender, marital status and so on), and determine the priori premium; then we adjuste driver's priemiums for the next year according to driver's historic claiming records, so we get the posteriori premiums. This approach is called Bonus-Malus system(BMS).This paper focuses on designing of bonus-malus system in automobile insurance using the principles of Beyes statistics. The majority of BMS presented up to now in the actuarial literature assign to each policyholder a premium based only on historic claiming records. In this paper, we incorporate in the above designing of BMS the important a priori information we have for each policyholder by introducing an exponential regression component. Thus we propose a generalized BMS that takes into consideration simultaneously the individual's characteristics, the number of his accidents and the exact level of severity for each accident. In most of classical bonus-malus systems we use quadratic loss functions to get the estimator for claim frequency and claim severity, that is the mean of the posterior structure function. In this paper we use an exponential loss function. And we can see that in the special case of c â†' 0, the best estimator under exponential loss function is also the mean of the posterior structure function, which corresponds to the classical exact credibility result using a quadratic loss function. So we get a more general result.Forthermore, we discussed the phenomenon of hunger for bonus in bonus-malus system; also we discussed the effect of a deductible and a policy limit for designing of BMS.