Extremes and robustness: a contradiction?

Stochastic models play an important role in the analysis of data in many different fields, including finance and insurance. Many models are estimated by procedures that lose their good statistical properties when the underlying model slightly deviates from the assumed one. Robust statistical methods can improve the data analysis process of the skilled analyst and provide him with useful additional information. For this anniversary issue, we discuss some aspects related to robust estimation in the context of extreme value theory (EVT). Using real data and simulations, we show how robust methods can improve the quality of EVT data analysis by providing information on influential observations, deviating substructures and possible mis-specification of a model while guaranteeing good statistical properties over a whole set of underlying distributions around the assumed one.