Tweedie分布在车险费率厘定中的应用

The Application of Tweedie Distribution in Auto Insurance Ratemaking

在车险费率厘定中经常假设索赔频率与索赔强度分别服从泊松分布与伽玛分布,即假设总索赔服从复合泊松-伽玛分布。为了估计各风险类的纯保费(即总索赔均值),通常做法是对索赔频率与索赔强度分别建立广义线性模型(GLM),进而得到各风险类的索赔频率与索赔强度的均值,然后把两均值简单相乘即可;另一种做法利用复合泊松-伽玛分布是Tweedie分布的特例这一性质,直接对总索赔建立广义线性模型,进而也可以得到各风险类的总索赔均值。本文阐述了两种建模方法在处理车险费率厘定问题时的区别,通过对来自国外、国内的两组数据进行实证分析,比较了两种建模方法的优劣,并得到了一些初步结论。

Auto insurance rate-making often assumes the claim frequency and claim severity follows Poisson distri- bution and Gamma distribution respectively, namely, the total claim follows compound Poisson-Gamma distribu- tion. Under this distributional assumption, generalized linear models （GLMs） are used to estimate the mean claim frequency and severity, then these estimators are simply multiplied to estimate the net premiums or the mean aggre- gate loss for various risks. Because the compound Poisson-Gamma distribution is a Tweedie distribution in nature, therefore another method is to establish a GLM for the total claims, and then arrive at the mean of total claims for various risks. The paper elaborated on the differences of these two modeling methods for auto insurance ratemaking. Through an exponential analysis of two data sets, both international and domestic, it compared their advantages and disadvantages and offered some initial conclusions.