Robust statistical inference for the chain-ladder method

Stochastic claims reserving in non-life insurance is a major actuarial issue and there is a growing awareness that modern statistical techniques should be used when calculating the overall outstanding claims reserve (i.e. the money that a company should set aside). A very broad literature is available concerning deterministic and stochastic models for forecasting future claims. To model the uncertainty of these claims reserves estimates, the bootstrapping technique is typically applied. Classical parametric statistical procedures work well if the underlying assumptions hold, but may become strongly unreliable when the shape of the true underlying model deviates from the assumed parametric model. Even small violations, which are rather the rule than the exception in practice, can give very misleading results. A typical violation is the presence of outliers in the data. Outliers are observations that do not follow the pattern indicated by the majority of the data. In this project, we will introduce state-of-the-art robust statistical techniques in the framework of stochastic claims reserving. This will lead to more reliable estimates of the claims reserves and their prediction errors. Furthermore, we will provide diagnostics to automatically detect the most influential observations in the data. Although clearly motivated by actuarial applications, some of our proposed methodologies will have broader applications and can also be applied on data from other fields.