# Robust bootstrap procedures for the chain-ladder method

## TL;DR

This paper develops and compares robust bootstrap methods for the chain-ladder claims reserving technique, addressing outlier sensitivity and improving inference accuracy in insurance reserve estimation.

## Contribution

It introduces and evaluates new robust bootstrap procedures tailored for the chain-ladder method, enhancing reliability in the presence of outliers.

## Key findings

- Robust bootstrap methods outperform classical ones with outlier data.
- The proposed procedures provide more accurate standard error estimates.
- Application to real data demonstrates practical effectiveness.

## 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.