考虑离群值的稳健链梯法  

Robust Chain Ladder Method Based on Outlying Values

作　　者：段白鸽[1] 张连增[2] 

机构地区：[1]复旦大学经济学院,上海200433 [2]南开大学经济学院,天津300071

出　　处：《数理统计与管理》2015年第6期989-1006,共18页Journal of Applied Statistics and Management

基　　金：中国博士后科学基金(2014M550206);国家自然科学基金面上项目(71271121);中央高校基本科研业务费专项资金(跨学科创新团队建设基金)(NKZXTD1101)

摘　　要：本文关注于流量三角形中的离群值问题,阐述了链梯法评估的索赔准备金对离群值具有高度依赖性。为了解决这一问题,考虑了一种稳健链梯法,包括计算进展因子的稳健方法和诊断并调整离群值的方法,并应用经典数据和比利时非寿险业务的真实数据进行了实证分析。数值结果表明,稳健链梯法具有优良性能,无论原始数据中存在单个或多个离群值,稳健链梯法都能有效识别并调整这些离群值,以减少离群值对索赔准备金估计的影响。在非寿险精算实务中,异常赔款额是完全有可能出现的,通过比较链梯法和稳健链梯法的评估结果,非寿险精算人员可以进一步分析导致异常赔款额背后的原因,并根据具体情况,采取合理的处理方法调整或保留异常赔款额,提高索赔准备金估计的准确性。The paper focuses on the appearance of outlying values in the run-off triangles of claims reserving. It is demonstrated that claims reserves based on chain ladder method are highly dependent on outlying values. In order to solve this problem, we consider robust chain ladder methods, including the robust method with development factors and the method of detect and adjust outlying values. On the basis, we apply the classical run-off triangles data and real run-off triangles data from a non-life insurance business in Belgium to have an empirical analysis. The numerical results show that the robust chain ladder method has an excellent performance. Regardless of there are single or multiple outlying values in the raw data, robust chain ladder method can also effectively identify and adjust these outliers, in order to reduce the impact of outliers on claims reserving. In the non-life actuarial practice several abnormal claims amount are likely to appear completely, some non-life actuaries can further analyze the hidden reasons of leading to abnormal claims amount by comparison the assessment results both chain ladder method and robust chain ladder method, and depended on the specific situation, they can also take a reasonable approach to adjust or retain the abnormal claims amount to improve the accuracy of the estimated claims reserve.

关 键 词：索赔准备金 离群值 稳健链梯法 残差诊断 敏感性分析 

分 类 号：F222[经济管理—国民经济] O212[理学—概率论与数理统计]