Approximating the admissible set in stochastic dominance

We first investigate the approximation question in a more abstract setting and then return to stochastic dominance. In Section 5 we study location-scale families of probability distributions because they are prospective limiting sets of alternatives for which two-parameter rules work exactly. In Section 6 we show that the compactness and continuity conditions in Sections 2 and 3 are satisfied for the two-parameter admissible sets. In Section 7 we show that the continuity results for general sets of alternatives extend to portfolios. Finally, in Section 8 we show how all the pieces can be combined to at least partially answer the original question. In Section 8 we also discuss several extensions, including rates of convergence and first-order stochastic dominance.