基于累积损失混合模型的贝叶斯保费研究

Bayesian Ratemaking Based on Mixed Models of Aggregated Claim Amount

商业车险的费率由先验费率和后验费率两部分构成。通常使用广义线性模型厘定先验费率,然后基于个体保单的索赔经验,应用贝叶斯方法计算后验费率。在传统方法中,一般是分别根据索赔次数或索赔强度建立费率厘定模型。本文基于个体保单的累积损失数据建立了一种混合回归模型,并在此基础上计算贝叶斯保费,为非寿险费率厘定提供了一种新方法。在先验费率的厘定中,基于个体保单的累积损失数据建立混合零调整逆高斯回归模型,代替了传统的Tweedie回归模型。对先验费率进行调整时,用个体保单的累积损失代替通常使用的索赔次数或索赔强度,规避了索赔次数与索赔强度之间的相依性可能造成的干扰。

The rate of commercial auto insurance consists of a priori rate and a posterior rate.The generalized linear models are usually used to determine the priori rate,and then based on the individual ＇s claim experience,the Bayesian method is used to calculate the posterior rate.Traditional ratemaking methods are usually based on claim numbers or claim severity.Based on the aggregated claim amounts of individual policies,this paper established a mixed regression model to calculate the Bayesian premium and provided a new method for non-.life insurance ratemaking.In the priori ratemaking process,the mixed zero-.adjusted inverse Gaussian regression model was established to replace the traditional Tweedie regression.In order to avoid the influence of possible dependence between the claim numbers and claim severity,aggregated claim amounts of individual policies were used to replace the claim numbers or claim severity in determining Bayesian premium.