Credibility premiums for the zero-inflated Poisson model and new hunger for bonus interpretation
- 作者：Jean-Philippe Boucher ; Michel Denuit
- 关键词：Credibility ; Count data ; Quadratic loss ; Exponential loss ; Zero-inflated models ; Number of accidents ; Hunger for bonus
- 刊名：Insurance ; Mathematics and Economics
- 出版年：2008
- 期刊代码：25_01676687
- 类别：mt
- 出版时间：April 2008
- 卷：42
- 期：2
- 页码：727-735
- 文件大小：934 K
摘要
The purpose of this paper is to explore and compare the credibility premiums in generalized zero-inflated count models for panel data. Predictive premiums based on quadratic loss and exponential loss are derived. It is shown that the credibility premiums of the zero-inflated model allow for more flexibility in the prediction. Indeed, the future premiums not only depend on the number of past claims, but also on the number of insured periods with at least one claim. The model also offers another way of analysing the hunger for bonus phenomenon. The accident distribution is obtained from the zero-inflated distribution used to model the claims distribution, which can in turn be used to evaluate the impact of various credibility premiums on the reported accident distribution. This way of analysing the claims data gives another point of view on the research conducted on the development of statistical models for predicting accidents. A numerical illustration supports this discussion.