Estimation of Extreme Risk Measures from Heavy-tailed distributions

Jonathan El Methni 1 Stephane Girard 1 Laurent Gardes 2
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : Value-at-risk, conditional tail expectation, conditional value-at-risk and conditional tail variance are classical risk measures. In statistical terms, the value-at-risk is the upper α-quantile of the loss distribution where α ∈ (0, 1) is the confidence level. Here, we focus on the properties of these risk measures for extreme losses (where α → 0 is no longer fixed). To assign probabilities to extreme losses it is assumed that we are in the case of heavy-tailed distributions. We also consider these risk measures in the presence of a covariate. Let us note that the presence of a covariate has already been investigated in extreme value theory. The main goal of this communication is to propose estimators of the above risk measures in the case of heavy-tailed distributions, for extreme losses, and to include a covariate in the estimation. The asymptotic distribution of our estimators is established and their finite sample behavior is illustrated on simulated data and on a real data set of pluviometrical measurements.
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Submitted on : Wednesday, July 17, 2013 - 12:24:11 PM
Last modification on : Wednesday, April 11, 2018 - 1:58:59 AM


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Jonathan El Methni, Stephane Girard, Laurent Gardes. Estimation of Extreme Risk Measures from Heavy-tailed distributions. EVA 2013 - 8th Conference on Extreme Value Analysis, probabilistic and statistical models and their applications, Jul 2013, Shanghai, China. pp.CDROM, 2013. 〈hal-00845527〉



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