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B1582
Title: Conditional marginal expected shortfall Authors:  Nguyen Khanh Le Ho - University of Southern Denmark (Denmark) [presenting]
Yuri Goegebeur - University of Southern Denmark (Denmark)
Armelle Guillou - Strasbourg university (France)
Jing Qin - University of Southern Denmark (Denmark)
Abstract: In the context of bivariate random variables $(Y^{(1)},Y^{(2)})$, the marginal expected shortfall, defined as $\mathbb E(Y^{(1)}|Y^{(2)} \ge Q_2(1-p))$ for $p$ small, where $Q_2$ denotes the quantile function of $Y^{(2)}$, is an important risk measure, which finds applications in areas like, e.g., finance and environmental science. We consider estimation of the marginal expected shortfall when the random variables of main interest $(Y^{(1)},Y^{(2)})$ are observed together with a random covariate $X$, leading to the concept of the conditional marginal expected shortfall. The asymptotic behavior of an estimator for this conditional marginal expected shortfall is studied for a wide class of bivariate distributions, with heavy-tailed marginal distributions, and where $p$ tends to zero at an intermediate rate. The finite sample performance is evaluated on a small simulation experiment.