非寿险费率厘定的索赔频率预测模型及其应用

Predictive Modeling of Claim Frequency in Non-Life Insurance Ratemaking

在非寿险分类费率厘定中,泊松回归模型是最常使用的索赔频率预测模型,但实际的索赔频率数据往往存在过离散特征,使泊松回归模型的结果缺乏可靠性。因此,讨论处理过离散问题的各种回归模型,包括负二项回归模型、泊松-逆高斯回归模型、泊松-对数正态回归模型、广义泊松回归模型、双泊松回归模型、混合负二项回归模型、混合二项回归模型、Delaporte回归模型和Sichel回归模型,并对其进行系统比较研究认为:这些模型都可以看做是对泊松回归模型的推广,可以用于处理各种不同过离散程度的索赔频率数据,从而改善费率厘定的效果;同时应用一组实际的汽车保险数据,讨论这些模型的具体应用。

Poisson regression model is the most popular predictive model of claim frequency in non--life insurance ratemaking. As the practical claim frequency often appears to be over--dispersed, the Poisson regression model may not produce credible result. The paper systematically analyzes and compares several over--dispersed regression models, including Negative Binomial regression, Poisson--inverse Gaussian regression, Poisson--Lognormal regression, generalized Poisson regression, double Poisson regression, mixed negative binomial regression, mixed binomial regression, Delaporte regression and Sichel regression. All these models extend Poisson regression model and may be used to cope with different kinds of over--dispersed claim frequency data and to improve ratemaking. At the end, the paper applies these models to an practical claim frequency data.