Generalized Almost Stochastic Dominance
32 Pages Posted: 18 Sep 2013 Last revised: 16 Apr 2014
Date Written: March 27, 2014
Almost stochastic dominance allows small violations of stochastic dominance rules to avoid situations where most decision makers prefer one alternative to another but stochastic dominance cannot rank them. While the idea behind almost stochastic dominance is quite promising, it has not caught on in practice. Implementation issues and inconsistencies between integral conditions and their associated utility classes contribute to this situation. We develop generalized almost second-degree stochastic dominance and almost second-degree risk in terms of the appropriate utility classes and their corresponding integral conditions, and extend these concepts to higher degrees. We address implementation issues and show that generalized almost stochastic dominance inherits the appealing properties of stochastic dominance. Finally, we defi ne convex generalized almost stochastic dominance to deal with risk-loving preferences. Generalized almost stochastic dominance could be useful in decision analysis, in empirical research (e.g., in fi nance), and in theoretical analyses of applied situations.
Keywords: Decision Analysis, Stochastic Dominance, Utility, Risk, Probability, Distribution Comparisons
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