准备金评估的随机性Munich链梯法及其改进——基于Bootstrap方法的实证分析

Stochastic Munich Chain Ladder Methods and Its Improvement in Claims Reserves

传统链梯法是未决赔款准备金评估最常用的确定性方法,Munich链梯法基于Mack模型的假设,利用已决赔款和已报案赔款的相关性调整进展因子,有效减少了链梯法分别基于已决赔款和已报案赔款得到的未决赔款准备金之间的差异。本文在系统介绍Munich链梯法的基础上,结合模型假设,提出了两种基于Bootstrap方法的随机性Munich链梯法,并通过精算实务中的数值实例应用R软件加以实证分析。本文的研究对保险公司准备金负债评估的准确性和充足性具有重要参考价值。

The traditional chain ladder method is the most used deterministic method in outstanding claims reserves. The Munich chain ladder method is based on the assumptions from Mack model. The main idea is to modify the development factors by making use of the correlation between the paid payments and incurred payments, so as to decrease the discrepancy between the outstanding claims reserves resulting from applying the traditional chain ladder methods separately. This paper begins with introducing the Munich chain ladder method, combined with the model assumptions, proposes two stochastic Munich chain ladder methods based on bootstrap, and obtain the predictive distribution of the total reserve. Numerical illustrations are provided, which are implemented with R language. The results obtained in the paper have important significance as to the accuracy and sufficiency of the reserves liability.