An Efficient Algorithm to Determine Stochastic Dominance Admissible Sets

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Abstract
Stochastic Dominance (SD) rules are playing an increasingly prominent role in the theory of choice under uncertainty. Its application areas include stock selection, capital budgeting, etc. The theory is important because it generates decision rules which are more generally applicable to these problems than are the traditional two parameter (mean-variance) rules employed in much of financial decision making. While they are theoretically sound, the SD rules are, until now, hard to implement because they require comparisons of probability distributions over their entire ranges. In this paper, we develop an algorithm that should remedy this situation. It exploits recent theoretical results from the Stochastic Dominance literature as well as several computational techniques to efficiently determine the SD admissible set of alternatives, which contains the optimal choices for all decision makers whose preferences satisfy reasonable economic criteria. As compared with the fastest code currently available, an implementation of our algorithm significantly reduces the computational time required to solve a problem of considerable size. These results indicate that, as a management tool, this algorithm can be applied to choice problems not previously thought solvable. For example, in the portfolio choice problem, which has an infinite choice set, the algorithm can provide reasonable approximations to the true set of optimal choices via the use of a suitably fine enough grid on the space of portfolios.

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