一个考虑了索赔事故责任比例的最优奖惩系统

An Optimal Bonus-Malus System Accounting for Responsibility Factor

在传统的汽车保险奖惩系统中,索赔次数是唯一的经验定价因素,但这不能真实地反映每位投保人的风险.针对这个问题,本文构建了一个同时考虑索赔次数和索赔事故责任比例两个因素的奖惩系统,并在假设任一保单持有人在以往年度的平均索赔事故责任比例服从[0,1]上的均匀分布的基础上,证明了这样构造的奖惩系统是最优的———能保持财务上的平衡.

The number of claims is the only empirical ratemaking factor in traditional motor insurance BMS. But claim numbers can not reflect each policyholder′s true risk. To this problem, we developed a new BMS in which both claim numbers and responsibility levels were considered. For a given policyholder, if the average responsibility level of all his/her past claims is assumed following a uniform distribution on [0,1], this BMS is proved to be optimal, that is, it can keep financial balance.