Séance Séminaire

Séminaire de Probabilités et Statistique

Nonparametric estimation of extreme risks from heavy-tailed distributions

Value-at-risk, conditional tail expectation, conditional value-at-risk and conditional tail variance are classical risk measures. For instance, the value-at-risk is defined as the upper alpha-quantile of the loss distribution where alpha is the confidence level. We propose nonparametric estimators of these risk measures for extreme losses, i.e. when alpha tends to zero and in the case of heavy-tailed distributions depending on covariates. The asymptotic distribution of the estimators is established and their finite sample behavior is illustrated both on simulated data and on a real data set of daily rainfalls in the Cévennes-Vivarais region (France). This is joint work with Jonathan El Methni (University of Geneva) and Laurent Gardes (University of Strasbourg).