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A New Robust Risk Measure: Quantile Shortfall

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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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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. Law School, Wuhan University, Wuhan, 430072, P.R. China

    You Li Chen

  2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P.R. China

    Yan Yan Liu

  3. School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, P.R. China

    Guang Cai Mao

  4. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073, P.R. China

    Yuan Shan Wu

  5. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P.R. China

    Fei Yan

Authors
  1. You Li Chen
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  2. Yan Yan Liu
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  3. Guang Cai Mao
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  4. Yuan Shan Wu
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  5. Fei Yan
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Corresponding authors

Correspondence to You Li Chen or Yan Yan Liu.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 11571263) and Fundamental Research Funds for the Central Universities (Grant No. 2042018kf0243)

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Chen, Y.L., Liu, Y.Y., Mao, G.C. et al. A New Robust Risk Measure: Quantile Shortfall. Acta. Math. Sin.-English Ser. 36, 1014–1024 (2020). https://doi.org/10.1007/s10114-020-9100-3

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  • DOI: https://doi.org/10.1007/s10114-020-9100-3

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