On consistency of stochastic dominance and mean-semideviation models

We analyze relations between two methods frequently used for modeling the c hoice among uncertain outcomes: stochastic dominance and mean-risk approach es. New necessary conditions for stochastic dominance are developed. These conditions compare values of a certain functional, which contains two compo nents: the expected value of a random outcome and a risk term represented b y the central semideviation of the corresponding degree. If the weight of t he semideviation in the composite objective does not exceed the weight of t he expected value, maximization of such a functional yields solutions which are efficient in terms of stochastic dominance. The results are illustrate d graphically.