汽车交通事故损失分布的尾部估计

由于巨额损失对保险公司的影响非常大,费率厘定过程中对极值分布的研究非常重视。本文从极值理论的角度出发,以上海市虹口区2003年的汽车交通事故损失数据为样本,探讨了损失分布的尾部估计方法,并利用该地区2006年的汽车交通事故损失对结论进行了验证。研究结果发现,广义帕雷托分布确实对损失额的尾部提供了较好的拟合,但这依赖于门槛值的恰当选择。传统的门槛值选择方法主观性较强,而通过重复多次的交叉验证技巧,我们可以估计广义帕雷托分布的最合适门槛值位置。

The Tail Estimate of Automobile Traffic Accident Loss Distribution

Because large loss have great effects on insurance companies, we pay more attention to the extreme loss in experience rating process. This paper starts from extreme value theory and investigates the method of tail estimation of loss distribution through the automobile traffic accident loss data of Shanghai Hongkou region for year 2003. Moreover, we validate the conclusion using the similar data for year 2006. We find that generalized Pareto distribution actually gives a better fit for the tail of loss data, but it depends on the right choice of threshold. The classical methods of threshold choice have some subjectivity, but through the repetition of cross-validation technique, we can estimate the most appropriate threshold position of generalized Pareto distribution.