索赔次数的开放式混合泊松分布研究

本文建立了索赔次数的多风险类别混合泊松模型。首先，考虑索赔次数的零膨胀、厚尾性和异质性等特征，建立风险类别待定的开放式混合泊松模型，开放式结构使该模型对实际数据的多样特征和风险类别具有良好的自适应性；其次，定义混合权重参数的iSCAD惩罚函数，实现对权重参数的筛选；最后，借助EM算法求得模型参数，实现对各风险类别下索赔次数的估计。借助iSCAD惩罚函数，给出最优混合数，避免传统混合模型中主观选择的弊端，克服传统混合模型中结构复杂、参数估计没有显式表达式、估计结果不便于解释等问题。基于三组风险特征多样数据的实证分析，本文发现该模型可以显著改进现有模型的拟合效果。

A Study on Open Mixed Poisson Distribution for Claim Frequency

This paper builds up an open mixed Poisson model with multiple risk categories of claim frequency. Firstly, an open mixed Poisson model is set up with risk categories to be defined, taking into account the characteristics, such as zero-inflated, heavy tailing and heterogeneity of the claim frequency. The open structure makes the model self-adaptable to various characteristics and risk categories in the actual data. Secondly, iSCAD penalty function defined with mixed weight parameters is applied to choose the suitable parameters. And finally, EM algorithm is used to acquire all the estimates of the claim frequency in different risk categories. By means of the iSCAD penalty function, the optimal mixed number is derived, keeping away from the subjective selection in the traditional mixed model, and solving the issues such as complicated structures, no explicit expression of parameter estimates and difficulty in explaining the estimates in the traditional mixed models. Based on the real data in three risk categories, the empirical study finds that the new model can significantly improve the fitting effects of the traditional ones.