A Study on the Combination of Deductible System with Bonus-Malus System

Bonus-Malus system in automobile insurance rewards claim-free policyholders by premium discounts and penalizes policyholders with claims by premium surcharges. The purpose of adopting bonus-malus system is to alleviate differences in risk propensity. A well-known side-effect of bonus-malus system is the tendency of policyholders to pay small claims themselves and not report them to their, in order to avoid future premium increases. This phenomenon is called hunger for bonus. In this paper, we introduces an alternative approach to the Bonus-Malus system in automobile insurance - the approach is based on a deductible theory; and then search for a proper way combining both of them. Also, we construct a new algorithm to determine the optimal strategy of the policyholder based on the proposed model.