Robust bootstrap procedures for the chain-ladder method

作     者：Peremans, Kris Segaert, Pieter Van Aelst, Stefan Verdonck, Tim 

作者机构：Katholieke Univ Leuven Dept Math Leuven Belgium 

出 版 物：《SCANDINAVIAN ACTUARIAL JOURNAL》 (斯堪的纳维亚保险计算杂志)

年 卷 期：2017年第000卷第10期

页      面：870-897页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 

基　　金：Internal Funds KU Leuven [C16/15/068, C24/15/001] Flemish Science Foundation (FWO) [1523915N] Research Foundation - Flanders (FWO) Flemish Government - department EWI 

主　　题：Claims reserving generalized linear models outliers inference Solvency II 

摘      要：Insurers are faced with the challenge of estimating the future reserves needed to handle historic and outstanding claims that are not fully settled. A well-known and widely used technique is the chain-ladder method, which is a deterministic algorithm. To include a stochastic component one may apply generalized linear models to the run-off triangles based on past claims data. Analytical expressions for the standard deviation of the resulting reserve estimates are typically difficult to derive. A popular alternative approach to obtain inference is to use the bootstrap technique. However, the standard procedures are very sensitive to the possible presence of outliers. These atypical observations, deviating from the pattern of the majority of the data, may both inflate or deflate traditional reserve estimates and corresponding inference such as their standard errors. Even when paired with a robust chain-ladder method, classical bootstrap inference may break down. Therefore, we discuss and implement several robust bootstrap procedures in the claims reserving framework and we investigate and compare their performance on both simulated and real data. We also illustrate their use for obtaining the distribution of one year risk measures.