最优奖惩系统的构建与评价——基于索赔次数与赔款金额的综合视角  

Construction and Evaluation of Optimal BMS:Comprehensive Perspective Based on Number of Claims and Individual Claim Size

作　　者：胡祥[1] 张连增 HU Xiang;ZHANG Lian-zeng(School of Finance,Zhongnan University of Economics and Law,Wuhan 430073,China;School of Finance,Nankai University,Tianjin 300071,China)

机构地区：[1]中南财经政法大学金融学院,湖北武汉430073 [2]南开大学金融学院,天津300071

出　　处：《数理统计与管理》2024年第2期369-380,共12页Journal of Applied Statistics and Management

基　　金：国家自然科学基金面上项目(71971216);高等学校学科创新引智基地(B21038)。

摘　　要：在商业车险中,奖惩系统是一种重要的后验费率调整机制,其基本原理是根据保单的历史索赔信息对续期保费进行调整。常见的奖惩系统仅考虑保单的历史索赔次数信息,但却忽视了赔款金额的影响,这可能会造成产品费率与其实际风险水平不匹配。本文综合考虑保单的索赔次数与赔款金额的信息,利用贝叶斯方法构建了新的最优奖惩系统,并运用极大似然法对模型参数进行估计。本文以我国商业车险中的一组索赔数据为例,进行实证研究。结果表明,对于不同赔款金额的保单,本文所构建的奖惩系统可通过不同的惩罚系数对其续期保费进行调整,从而有效提高后验费率厘定的准确性。Bonus-malus system(BMS)is a premium adjustment mechanism widely used in the commercial auto insurance to set the posterior premium for the next contract period based on a policyholder's claim history.It is usually assumed that the a priori premium assigned to each policyholder adjusts based only on the number of claims.However,not all accidents produce the same individual claim size and thus it does not seem fair to penalize all policyholders in the same way when claims are presented.By a Bayesian methodology,this paper is devoted to the design of BMS involving different sources of a priori information,including the experiences of the number of claims and the individual claim size.The parameters of the BMS are estimated by applying the maximum likelihood method.An empirical analysis using an auto insurance claims database from an insurance company of China is presented.The results indicate that the proposed models could distinguish between claims with different size and then penalize policyholders depending on their experience with respect to the different types of claim,which effectively improve the accuracy of the a posteriori ratemaking.

关 键 词：奖惩系统 贝叶斯方法 索赔次数 赔款金额 后验费率 

分 类 号：F222.3[经济管理—国民经济] O212[理学—概率论与数理统计]