基于联合定价模型的奖惩因子的扩展与比较  

Extension and Comparison of Bonus-Malus Factor Based on Joint Pricing Models

作　　者：谢远涛[1] 李政宵[2] 

机构地区：[1]对外经济贸易大学保险学院,北京100029 [2]中国人民大学统计学院,北京100872

出　　处：《统计与信息论坛》2015年第6期33-39,共7页Journal of Statistics and Information

基　　金：国家自然科学基金项目<风险信息共享背景下的个体风险评估研究>(71303045);对外经济贸易大学中央高校基本科研业务费专项资金资助(15YQ09)

摘　　要：信度模型是经验费率厘定的主要方法,其缺陷在于隐含的正态分布假设并不适用于索赔次数,同时也无法分析费率因子对预期保费的影响。若将信度模型与广义线性混合模型相结合,同时考虑保单已知的风险特征信息和潜在的个体风险特征信息,将正态分布假设推广到泊松分布,放宽随机效应假设,即可构建一种扩展的联合定价模型。扩展的联合定价模型不仅能解决定价过程中风险信息重叠的问题,其预测值还具有类似信度模型"收缩估计"的性质。对一组保单索赔次数数据的研究发现,扩展的联合定价模型(泊松-伽马模型)对索赔次数的拟合更加合理,解决了奖惩因子的"过度奖惩"的问题,有效改进了预测结果。Credibility model is the main method of experience ratemaking. However, traditional credibility model has own limitation as it assumes the response variable follows normal distribution. This implicit assumption of normal distribution does not describe the number of claims and other discrete data reasonably, and cannot consider the impact of risk factors in calculating premium. Meanwhile, as an important method in classification retaking, generalized linear mixed model can be combined with credibility theory. In this way, it can solve these problems effectively. In this paper, we take into account both risk factors and unobserved individual risk characteristics and extend the normal distribution to Poisson distribution, constructing an extension of the joint pricing model, which can fit number of claims more precisely. The extension of joint pricing model can not only solve the pricing process information overlap or error amplification issues, but also presents the credibility-like shrinkage predictor toward the mean in response to low credibility. The empirical study suggests that the extension of joint pricing model with Poisson-Gamma distribution shows the stronger fitting criterion and less mean standard error.

关 键 词：联合定价模型 重复奖惩 奖惩因子 收缩估计 

分 类 号：O212[理学—概率论与数理统计] F840.4[理学—数学]