Minimal Quantile Functions Subject to Stochastic Dominance Constraints

Abstract

We consider a problem of finding an SSD (second-order stochastic dominance)-minimal quantile function subject to the mixture of FSD (first-order stochastic dominance) and SSD constraints. The SSD-minimal solution is explicitly worked out and has a close relation to the Skorokhod problem. This result is then applied to explicitly solve a risk minimizing problem in financial economics.