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A Weissman-type estimator of the conditional marginal expected shortfall

Abstract : The marginal expected shortfall is an important risk measure in finance, which has been extended recently in the case where the random variables of main interest (Y^{(1)}, Y^{(2)}) are observed together with a covariate X \in R^d. This leads to the concept of conditional marginal expected shortfall. It is defined as \theta_p(x_0)=E[Y^{(1)} | Y^{(2)} \geq Q_{Y^{(2)}}(1-p|x_0); x_0], where p is small and Q_{Y^{(2)}} denotes the quantile function of Y^{(2)}. In this paper, we propose an estimator for \theta_p(x_0) allowing extrapolation outside the Y^{(2)} - data range, i.e., valid for p < 1/n. The main asymptotic properties of this estimator have been established, using empirical processes arguments combined with the multivariate extreme value theory.
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https://hal.archives-ouvertes.fr/hal-02613135
Contributor : Armelle Guillou <>
Submitted on : Tuesday, May 19, 2020 - 6:53:21 PM
Last modification on : Thursday, May 21, 2020 - 1:41:11 AM

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Yuri Goegebeur, Armelle Guillou, Nguyen Khanh Le Ho, Jing Qin. A Weissman-type estimator of the conditional marginal expected shortfall. 2020. ⟨hal-02613135⟩

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