我国商业车险奖惩系统的构建与评价

在商业车险定价中,通常根据保单的先验风险特征信息建立广义线性模型来厘定先验费率,然后根据保单的历史索赔信息应用奖惩系统对先验费率进行调整.本文基于一组商业车险保单2010-2015年的索赔次数数据,分别在泊松-伽马分布假设和负二项-贝塔分布假设下构建了奖惩系统,运用贝叶斯方法和极大似然法估计了模型参数,测算了奖惩系数,并与我国现行的奖惩系数进行了比较.实证研究结果表明,我国现行奖惩系统的设计结构比较单一,对保单经验索赔信息的使用不充分,且奖惩幅度过于温和.本文构建的奖惩系统充分利用了保单的先验风险特征信息与历史索赔信息,有效避免了对保单的重复性奖励和惩罚,提高了费率厘定结果的准确性和合理性.

Construction and evaluation of BMS for automobile insurance in China

In ratemaking of automobile insurance, insurers usually first charge the premium by using generalized linear models that can accounts for the prior information of individual polices and then adjust the premium based on the numbers of his claims in the past years by using bonus-malus system. This paper establishes the optimal bonus-malus system based on Poisson-Gamma distribution and Negative Binomial-Beta distribution to analyze the datasets collected by an insurance company in China, which contains claim information from year 2010 to 2015. We apply both the maximum likelihood method and Bayesian approach to calculate the bonus-malus factors. The paper shows that the current bonus-malus system in China is too simple and the claim information of insureds is not completely used. Moreover, the current BMS in China gives too less bonus for good drivers and too less malus for bad drivers. The optimal BMS we proposed in the paper takes into account simultaneously the prior characteristics and claim numbers of each policyholder, effectively avoiding the repeated bonus or malus for the premium, making the ratemaking process more reasonable and more accurate.