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Nonparametric estimation of extreme risks from heavy-tailed distributions

Jonathan El Methni 1 Laurent Gardes 2 Stéphane Girard 1
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : Value-at-risk, conditional tail expectation [1], conditional value-at-risk [4] and conditional tail variance [5] are classical risk measures. For instance, the value-at-risk is de ned as the upper alpha- quantile of the loss distribution where alpha is the confi dence level. In this communication, we propose nonparametric estimators of these risk measures for extreme losses, i.e. when alpha converges to0 and in the case of heavy-tailed distributions depending on covariates. Let us note that the presence of covariates in extreme value theory has already been investigated for instance in [2, 3]. The asymptotic distribution of the estimators is established and their fi nite sample behavior is illustrated both on simulated data and on a real data set of daily rainfalls in the Cevennes-Vivarais region (France). [1] Artzner, P., Delbaen, F., Eber, J.M., and Heath, D. (1999) Coherent measures of risk, Mathematical Finance, 9, 203-228. [2] Daouia, A., Gardes, L., Girard, S. and Lekina, A. (2011) Kernel estimators of extreme level curves, Test, 20, 311-333. [3] Daouia, A., Gardes, L. and Girard, S. (2013) On kernel smoothing for extremal quantile regression, Bernoulli, to appear. [4] Rockafellar, R.T., Uryasev, S. (2000) Optimization of conditional value-at-risk, Journal of Risk, 2, 21-42.
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Submitted on : Tuesday, September 17, 2013 - 2:23:53 PM
Last modification on : Thursday, January 20, 2022 - 5:30:15 PM


  • HAL Id : hal-00862759, version 1



Jonathan El Methni, Laurent Gardes, Stéphane Girard. Nonparametric estimation of extreme risks from heavy-tailed distributions. Extremes in Vimeiro Today, Sep 2013, Vimeiro, Portugal. ⟨hal-00862759⟩



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