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Title: A bias-reduced version of the Weissman estimator for extreme value-at-risk Authors:  Jonathan El Methni - Universite Paris Cite (France) [presenting]
Stephane Girard - Inria (France)
Abstract: One of the most popular risk measures is the Value-at-Risk, which in statistical terms corresponds to the upper $\alpha$-quantile of the distribution where $\alpha \in (0,1)$ is the risk level. We are interested in estimating this risk measure at an extreme level which means when $alpha$ tends to 0 as the sample size goes to infinity. If the random variable of interest has a heavy-tailed distribution, a common estimator of the Value-at-Risk at extreme levels is the Weissman estimator. The latter is based on two estimators: an order statistic to estimate an intermediate quantile and an estimator of the tail index. The usual practice is to select the same intermediate sequence for both estimators. We show how an adapted choice of two different intermediate sequences leads to a reduction of the asymptotic bias associated with the resulting Weissman estimator. Our approach is compared to other bias-reduced estimators of the extreme Value-at-Risk both on simulations and on a financial real dataset.