零膨胀泊松模型的改进在零次索赔建模中的应用

零膨胀是非寿险精算中的一种常见现象,国内外许多学者对此进行了研究分析,而最具影响力的方法是零膨胀泊松模型与Hurdle模型,但这两个方法在区分零之间的差别时存在不足。实际中,产生零次索赔的保单持有人并非全部同质,如何提取零中所包含的信息对保险公司来说是重要的。鉴此,基于零膨胀泊松模型与Hurdle模型的思想,提出修正的零膨胀泊松模型,并利用非寿险精算中的实际数据,对新模型进行了拟合分析。与零膨胀泊松模型拟合结果的比较说明,修正的零膨胀模型在零的处理上更符合实际情况,更能体现零中所包含的信息。

An Application of Adjusted Zero-inflated Poisson Model to Zero Claims

Zero-inflation is a common phenomenon in non-life insurance and the most powerful tools to analysis it are the zero-inflated Poisson（ZIP） model and Hurdle model.Based on reasons about engendering the zero-inflation,this paper points out the drawbacks of zero-inflated Poisson model and Hurdle model.However,it is important for an insurer to distinguish the difference between zeroes.So,based on the ideas of zero-inflated Poisson model and Hurdle model,we give our definition of the adjusted zero-inflated Poisson（AZIP） model and use it to fit actual motor insurance data.Through analysing and comparing with zero-inflated Poisson model,the conclusion is that the adjusted zero-inflated Poisson model is more appropriate in dealing with the zeroes.