A New Robust Risk Measure: Quantile Shortfall |
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| Authors: | You Li CHEN Yan Yan LIU Guang Cai MAO Yuan Shan WU Fei YAN |
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| Affiliation: | 1. Law School, Wuhan University, Wuhan 430072, P. R. China;2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China;3. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China;4. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, P. R. China;5. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China |
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| Abstract: | Among recent measures for risk management, value at risk (VaR) has been criticized because it is not coherent and expected shortfall (ES) has been criticized because it is not robust to outliers. Recently,[Math. Oper. Res., 38, 393-417 (2013)] proposed a risk measure called median shortfall (MS) which is distributional robust and easy to implement. In this paper, we propose a more generalized risk measure called quantile shortfall (QS) which includes MS as a special case. QS measures the conditional quantile loss of the tail risk and inherits the merits of MS. We construct an estimator of the QS and establish the asymptotic normality behavior of the estimator. Our simulation shows that the newly proposed measures compare favorably in robustness with other widely used measures such as ES and VaR. |
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| Keywords: | Nonparametric estimation quantile shortfall risk measure robust |
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