Robust bootstrap procedures for the chain-ladder method

Abstract

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.

Keywords:

• Claims reserving
• generalized linear models
• outliers
• inference
• Solvency II

Notes

No potential conflict of interest was reported by the authors.

1 Note that we define the total reserve R as the total amount of the incremental claims in the lower right triangle (as in key references England & Verrall (2002) and Wüthrich & Merz (2008)), but in practice the final reserve is an amount set by the insurer based on this value.

2 http://www.casact.org/research/index.cfm?fa=loss_reserves_data.

Additional information

Funding

This work was supported by the Internal Funds KU Leuven [grant number C16/15/068], [grant number C24/15/001]; the Flemish Science Foundation (FWO) [grant number 1523915N]. The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation – Flanders (FWO) and the Flemish Government – department EWI.