There is a duality theory connecting certain stochastic orderings between cumulative distribution functions F1 , F2 and stochastic orderings between their inverses F −1 , F −1. This underlies some theories of utility in the case of the cdf and deprivation indices in the case of the inverse....

In this paper we compare overall as well as downside risk measures with respect to the criteria of first and second order stochastic dominance. While the downside risk measures, with the exception of tail conditional expectation, are consistent with first order stochastic dominance, overall risk...