相依风险条件下的汽车保险定价模型  

Pricing Models of Automobile Insurance with Dependent Risks

作　　者：李政宵[1] 孟生旺[2,1] 

机构地区：[1]中国人民大学统计学院,北京100872 [2]中国人民大学应用统计科学研究中心,北京100872

出　　处：《保险研究》2016年第7期68-77,共10页Insurance Studies

基　　金：国家自然科学基金项目"考虑风险相依的非寿险精算模型研究"(71171193)

摘　　要：车险保费由纯保费和附加保费两部分构成,其中纯保费往往占到保费的60%左右,主要用于覆盖保险公司的期望赔付金额,因此,纯保费预测是汽车保险定价的关键和基础。泊松-伽马模型和Tweedie模型是纯保费预测的两种主流模型。它们之间既有联系,又有区别。泊松-伽马模型中隐含了索赔频率与案均赔款之间相互独立的假设。当索赔频率与案均赔款之间存在负相依关系时,泊松-伽马模型可能高估保费,而存在正相依关系时可能低估保费。本文通过数据模拟的方法,分析了相依性对两种模型的影响,发现无论相依性如何变化,两种模型的对费率因子的估计值几乎相等。最后,通过一组实际数据的实证研究表明,两种模型的预测能力不相上下,其中Tweedie模型的预测误差略小,而泊松-伽马模型的稳健性略高。The premium of automobile insurance contains two parts ： pure premium and loading premium. Pure pre- mium usually accounts for 60 percent of the premium, which is used to cover the expected claims. Therefore, predic- ting the pure premium is the key task of automobile insurance ratemaking. Poisson-Gamma model and Tweedie model are two main methods in predicting the pure premium. They are both related and different. The Poisson- Gamma model implies the independent assumptions between claim frequency and claim amount. In fact, the inde- pendent assumptions in Poisson-Gamma model may lead to underestimation or overestimation for the pure premium when negative dependence or positive dependence exists. In this paper, we applied the Monte Carlo simulation to analyze the impact of different dependence on robustness of both models. It was found that no matter how the de- pendence varied, the estimated premium rate factors by these two models were almost equal. We also applied both models to a set of insurance data and the result showed that their accuracy of prediction was similar, with the Tweeg- die model having a slightly lower error while the Poisson-Gamma model having a stronger robustness.

关 键 词：相依风险 Tweedie模型 泊松-伽马模型 纯保费 汽车保险 

分 类 号：O212[理学—概率论与数理统计]