Necessary and sufficient conditions for stochastic dominance

The mathematical concept of stochastic dominance was introduced to describe preference of one random gain over another. We show that for bounded gains apart from the mathematical definition there is a more natural interpretation: one gain dominates another if the expected values of a class of non-decreasing functions are larger. This class of functions includes all natural utility functions. Some special choices give the necessary conditions for stochastic dominance derived by W.H. Jean (1980, 1984). We also provide some easy to check sufficient conditions for stochastic dominance. It is argued that if the difference of the densities of two gains has n-1 sign changes and certain moment relations are satisfied, one dominates the other stochastically for order n