On expectiles and almost stochastic dominance

We investigate the relationship between almost first order stochastic dominance (AFSD), the statistical functionals called expectiles, and the corresponding expectile-based monetary risk measure. From a methodological point of view, we show that expectiles provide a ready-to-be-used criterion for the comparison between a deterministic and a random payoff in the sense of AFSD. Furthermore, we obtain a consistency result for expectile-based monetary risk measures with respect to the AFSD ordering. Finally, we discuss applications to robustify some utility-based risk management procedures when there is uncertainty on the utility function to be considered. This includes preference robust portfolio optimization problems and worst-case shortfall risk measures.