分位数方法下寿险风险边际的计量实现研究

Measuring Life Insurance Risk Margins with Quantile Method

在偿二代制度下,当前寿险精算实务中利用分位数法计算风险边际的一个难点是确定损失分布,因此旨在为保险实务界引入行之有效的解决方法。这些方法主要以非参数统计学为核心,在文中以早期退保率波动带来的损失风险为例,对于这些非参方法进行比较。最终发现,大样本情形时利用kernel估计替代法估计一般水平(如75%)的风险边际非常适合,小样本情形可以用bootstrap百分位法;但是对于极高水平(如99.5%)的风险边际这些方法均不太理想;在退保率风险上,早期严重退保使得后期准备金的方差加大,不稳定性增强,同时75%水平的风险边际的峰值也出现在后期,其数值占到年保费的近一半。

Under the C-ROSS system,the quantile method can be used to measure risk margin,but how to deter- mine the distribution of losses is one of the difficult points. This paper introduced nonparametric statistical approa- ches to solve this problem. It used the loss risk due to early surrender rate fluctuations as an example to simulate the measurement of risk margin. It arrived at the conclusion that with big sample data, the Kernel estimation plug-in method was appropriate for calculating the normal level （such as 75% ） risk margin;for small sample data, the Bootstrap-percent method was suitable. However, for extremely high level risk margin, such as 99.5 %, neither method was desirable. For the surrender rate risk, severe surrender problem at the early stage would widen the vari- ance of later part liabilities, and increase instability. Moreover, the 75% level of risk margin peaked at the late stage, accounting for nearly half of the annual premium.