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Kernel estimation of extreme risk measures for all domains of attraction

Jonathan El Methni 1 Stéphane Girard 2 Laurent Gardes 3
2 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 : 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 we assume that the distribution satisfies a von-Mises condi- tion which allows us to work in the general setting, whether the extreme- value index is positive, negative or zero i.e. for all domains of attraction. We also consider these risk measures in the presence of a covariate. The main goal of this communication is to propose estimators of the above risk measures for all domains of attraction, for extreme losses, and to include a covariate in the estimation. The estimation method thus combines non- parametric kernel methods with extreme-value statistics. 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 daily rainfall.
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Submitted on : Monday, May 9, 2016 - 3:43:06 PM
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  • HAL Id : hal-01312846, version 1


Jonathan El Methni, Stéphane Girard, Laurent Gardes. Kernel estimation of extreme risk measures for all domains of attraction. Extremes, Copulas and Actuarial Sciences, Feb 2016, Marseille, France. ⟨hal-01312846⟩



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