Non-Emptyness of Stochastic Dominance Efficient Sets via Stochastic Spanning

We derive sufficient conditions for non-emptyness of the efficient set for Stochastic Dominance Relations, commonly applied in Economics and Finance, over sets of distributions on the real line. We do so via the use of the concept of stochastic spanning and its characterization via a saddle type property. Under the appropriate framework sufficiency takes the form of semi-continuity of some related functional. In some cases this boils down to mild uniform moment existence conditions