Stochastic Dominance: Convexity and Some Efficiency Tests

This paper points out the importance of Stochastic Dominance (SD) efficient sets being convex. We review classic convexity and efficient set characterization results on SD efficiency of a given portfolio relative to a diversified set of assets and generalize them in the following aspects. First, we broaden the class of individual utilities in Rubinstein (1974) that lead to two-fund separation. Secondly, we propose a linear programming SSD test that is more efficient than that of Post (2003) and expand the SSD efficiency criteria developed by Dybvig and Ross (1982) onto the Third Order Stochastic Dominance and further to Decreasing Absolute and Increasing Relative Risk Aversion Stochastic Dominance. The efficient sets for those are finite unions of convex sets.