Robust bootstrap techniques for claims reserving

Non-life insurers are often faced with the challenge of estimating the future reserves necessary to handle claims that are not fully settled. A well-known and popular technique to obtain reserve estimates for these outstanding claims is the (deterministic) chain-ladder method. Exactly the same estimates can also be obtained by applying special cases of generalized linear models. To obtain a prediction interval for the outstanding claims, we need an estimate for the variance of the resulting reserve estimate. Computing analytic expressions for the variance is notoriously difficult and bootstrap methodology offers a simple and popular alternative. However, classical 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 classical future claim estimates. Even when paired with robust estimators for generalized linear models, classical bootstrap estimators may break down. We present and discuss some popular and state of the art robust bootstrap procedures in the claims reserving framework. Their performance will be investigated in a simulation study and on real data.status: publishe