Wanted: A Test for FSD Optimality of a Given Portfolio

FIRST-ORDER STOCHASTIC DOMINANCE (FSD) is one of the fundamental concepts of decision making under uncertainty, relying only on the assumption of nonsatiation, or decision makers preferring more to less. There exist well-known, simple algorithms for establishing FSD relationships between a pair of choice alternatives. Unfortunately, these algorithms have limited use in applications with more than two choice alternatives. The analysis of investment portfolios is one such application; investors generally can form a large number of portfolios by diversifying across individual assets. For such applications, there is a need to develop an algorithm for establishing if a given portfolio represents the optimal solution for at least some nonsatiable investor, i.e., is in the FSD optimal set.