On Determination of Stochastic Dominance Optimal Sets
基于Fishburn的凸随机占优条件，提出线性规划算法将离散收益分布划分到一阶和二阶随机占优最优集，并定义超凸随机占优处理三阶占优，应用于896只证券收益数据，发现一阶、二阶、三阶最优集分别含454、25、13个分布。
ABSTRACT Applying Fishburn's [4] conditions for convex stochastic dominance, exact linear programming algorithms are proposed and implemented for assigning discrete return distributions into the first‐ and second‐order stochastic dominance optimal sets. For third‐order stochastic dominance, a superconvex stochastic dominance approach is defined which allows classification of choice elements into superdominated, mixed, and superoptimal sets. For a choice set of 896 security returns treated previously in the literature, 454, 25, and 13 distributions are in the first‐, second‐, and third‐order convex stochastic dominance optimal sets, respectively. These optimal sets compare with admissible first‐, second‐, and third‐order stochastic dominance sets of 682, 35, and 19 distributions, respectively. The applicability of superconvex stochastic dominance for continuous distributions defined over a bounded interval is then shown. The difficulties in identifying the elements of the superdominated set for distributions defined over the entire real line are demonstrated in the determination of the dominated choices for a set of normally distributed mutual fund returns previously examined by Meyer [9]. Specifically, we find that the dominated set determined by Meyer is too large.