With the development of financial risk management, the notion of convex risk measures has been proposed and has gained more and more attentions. Utility-based shortfall risk (SR), as a specific and important class of convex risk measures, has become popular in recent years. In this paper we...

Estimating quantile sensitivities is important in many optimization applications, from hedging in financial engineering to service-level constraints in inventory control to more general chance constraints in stochastic programming. Recently, Hong (Hong, L. J. 2009. Estimating quantile...