摘要
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.
基金
Supported by the National Natural Science Foundation of China(Grant No.11571263)
Fundamental Research Funds for the Central Universities(Grant No.2042018kf0243)
We thank the referees for their time and comments.
