In order to rank investments under uncertainty, the most widely used method is mean variance analysis. Stochastic dominance is an alternative concept which ranks investments by using the whole distribution function. There exist three models: first-order stochastic dominance is used when the distribution functions do not intersect, second-order stochastic dominance is applied to situations where the distribution functions intersect only once, while third-order stochastic dominance solves the ranking problem in the case of double intersection. Almost stochastic dominance is a special model. Finally we show that the existence of arbitrage opportunities implies the existence of stochastic dominance, while the reverse does not hold.
Stochastic Dominance Option Bounds and Nth Order Arbitrage Opportunities