二维GPSJ分布类及其在保险中的应用

The Bivariate GPSJ Class and Its Application in Insurance

本文给出的二维GPSJ分布类(即GPSJ2)在保险领域应用范围较广,如由机动车辆保险由财产损失索赔次数和人身伤亡索赔次数所组成的模型、超额再保险中的由自留保单数和分出报单数所组成的二维模型等。本文在GPSJ1类基础上研究二维GPSJ类,本文给出了此分布类的定义、背景意义、概率计算的递推公式,同时还对各参数的最大似然估计值的求解过程进行了分析。本文最后将这一模型应用于一组机动车辆赔付次数数据,考虑了由财产损失索赔次数、人身伤亡索赔次数组成的二维模型,拟合效果令人满意。

The model presented in this paper is very useful in insurance,especially for frequencies of property claims/frequencies of liability claims model,frequencies of retention claims/frequencies of excess treaty claims model in reinsurance.We study a class of bivariate GPSJ distributions by extending the GPSJ class from the uni-variate case to the bivariate case.We also show how to obtain the recursive formula of its probabilities.The study typically extends the use of some bivariate distributions appeared in literatures.Finally we employ this class to an application and the fitting effect is satisfying.