This paper aims to extend the results by Ross (1981) [15] and by Modica and Scarsini (2005) [13] to stochastic dominance of degree 4 and over. Specifically, it is shown that Ross' approach can be extended to any order of risk attitude beyond the generalization proposed by Modica and Scarsini by...

Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable dominates via ith-order stochastic dominance for i=M,N. We show that the 50-50 lottery dominates the lottery via (N+M)th-order stochastic dominance. The basic idea...