零膨胀广义泊松回归模型与保险费率厘定

在保险产品的分类费率厘定中,最常使用的模型之一是泊松回归模型.当损失数据存在零膨胀(zero-in flated)特征时,通常会采用零膨胀泊松回归模型.在零膨胀泊松回归模型中,一般假设结构零的比例参数φ为常数,不受费率因子的影响,这有可能背离实际情况.假设参数φ与费率因子之间存在一定关系,并在此基础上建立了零膨胀广义泊松回归模型,即Z IGP(τ)回归模型.通过对一组汽车保险损失数据的拟合表明,Z IGP(τ)回归模型可以有效地改善对实际数据的拟合效果,从而提高费率厘定结果的合理性.

Zero-Inflated Generalized Poisson Regression Model and Its Application to Insurance Ratemaking

Poisson regression model is widely used in insurance classification ratemaking.When the data appear to be zero-inflated,zero-inflated poisson regression model will be applied,and the proportion parameter φ of structural zeros is usually supposed to be constant and not affected by rating factors.Nevertheless,this may deviate from reality.So we suppose some rating factors may have an effect on φ and propose a new zero-inflated generalized Poisson regression model,i.e., ZIGP(τ) model.At the end of the paper,we apply ZIGP(τ) model to a data set of automobile insurance loss and the result shows that the goodness-of-fit can be effectively improved,so it may result in a more reasonable insurance rate.