Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), it is now known that their...

This paper investigates whether and when fractional degree stochastic dominance rules can inherit the invariance properties of integer-degree stochastic dominance. Within a general formulation, we first show that it is impossible for fractional degree stochastic dominance to obey all the six...

Two notions of fractional stochastic dominance are recently proposed by Muller et al. (2017) and Huang et al. (2020), respectively. Our main objective is to understand the comparative advantages of the two notions, as well as their suitability in different contexts, by establishing several new...