Conditional marginal expected shortfall

Abstract : In the context of bivariate random variables (Y^{(1)},Y^{(2)}), the marginal expected shortfall, defined as 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 conditional bivariate distributions, with heavy-tailed marginal conditional distributions, and where p tends to zero at an intermediate rate. The finite sample performance is evaluated on a small simulation experiment. The practical applicability of the proposed estimator is illustrated on flood claim data.
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Submitted on : Saturday, November 30, 2019 - 10:53:56 AM
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Yuri Goegebeur, Armelle Guillou, Nguyen Khanh Le Ho, Jing Qin. Conditional marginal expected shortfall. 2019. ⟨hal-02272392v2⟩

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