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...
