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On the extrapolation limits of extreme-value theory for risk management

Clément Albert 1 Anne Dutfoy 2 Stéphane Girard 1
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann
Abstract : In the risk management context, the extreme-value methodology consists in estimating extreme quantiles-one hundred years return period or more-from an extreme-value distribution adjusted on data. In this communication, we quantify the extrapolation limits associated with extreme quantile estimations. To this end, we focus on the framework of the block maxima method and we study the behaviour of the relative approximation error of a quantile estimator dedicated to the Gumbel attraction domain. We give necessary and sufficient conditions for the error to converge towards zero and we provide a first order approximation of the latter. We show that extrapolations can be greatly limited depending on the data distribution.
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Clément Albert, Anne Dutfoy, Stéphane Girard. On the extrapolation limits of extreme-value theory for risk management. MMR 2017 - 10th International Conference on Mathematical Methods in Reliability, Jul 2017, Grenoble, France. pp.5. ⟨hal-01571099⟩

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