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Estimation of the expected shortfall given an extreme component under conditional extreme value model

Research paper by Rafał Kulik, Zhigang Tong

Indexed on: 09 Sep '18Published on: 05 Sep '18Published in: Extremes



Abstract

Abstract For two risks, X and Y, the Marginal Expected Shortfall (MES) is defined as \(\mathbb {E}[Y\mid X>F_{X}^{\leftarrow }(1-p)]\) , where F X is the distribution function of X and p is small. In this paper we establish consistency and asymptotic normality of an estimator of MES on assuming that (X, Y ) follows a Conditional Extreme Value (CEV) model. The theoretical findings are supported by simulation studies. Our procedure is applied to some financial data.