基于进展时间和操作时间的两步广义线性混合模型非寿险准备金估计

Two-Step Generalized Linear Mixed Models Based on Development Time and Operational Time in Non-life Insurance Loss Reserving

对于非寿险准备金估计,传统流量三角形进展年的选择一直饱受争议,过长时易因数据不足难以估计,过短时可能会出现零赔付的情况。引入操作时间可以解决这一问题,但直接计算的操作时间实际上被严重高估。为此基于信度思想,使用个体信息将保单分组,建立两步广义线性混合模型,首先引入进展时间估计操作时间,再使用操作时间估计指定时间段内的未决赔款准备金。使用某非寿险公司的车损数据进行实证分析,并将该模型与使用传统流量三角的广义线性模型进行对比,结果均表明该模型效果甚佳。

It is very difficult to determine the length of development year in traditional run - off triangles for non - life insurance reserve estimation. It is either too long to get enough data for estimation or too short to ensure each development year have a claim. The introduction of operational time is a solution to this problem. Unfortunately, the operational time is highly overestimated when it is directly computed. Base on the credibility theory, we grouped policies by individual information, and created a two -step GLMM model. Firstly, we introduced the development time to estimate the operational time, then we used the operational time to estimate the IBNR for a specific period. Finally, we conducted an empirical analysis of vehicle damage insurance of a non - life insurer and made a comparison between this model and the GLM using traditional run - off triangles. Both analyses indicated that this model produced a better result.