Stochastic Dominance: Convexity and Some Efficiency Tests

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