On Determination of Stochastic Dominance Optimal Sets
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- Author(s): VIJAY S. BAWA, JAMES N. BODURTHA, M. R. RAO, HIRA L. SURI
- Published: Apr 30, 2012
- Pages: 417-431
- DOI: 10.1111/j.1540-6261.1985.tb04965.x
Applying Fishburn's  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 . Specifically, we find that the dominated set determined by Meyer is too large.