What If We Only Have Approximate Stochastic Dominance?

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Hung T. Nguyen, New Mexico State University - Main CampusFollow
Songsak Sriboonchitta, Chiang Mai UniversityFollow

Publication Date

7-2014

Comments

Technical Report: UTEP-CS-14-38a

Published in: Van-Nam Huynh, Vladik Kreinovich, Songsak Sriboonchitta, and Komsan Suriya (eds.) Econometrics of Risk, Springer Verlag, Berlin, Heidelberg, 2015, pp. 53-61.

Abstract

In many practical situations, we need to select one of the two alternatives, and we do not know the exact form of the user's utility function -- e.g., we only know that it is increasing. In this case, stochastic dominance result says that if the cumulative distribution function (cdf) corresponding to the first alternative is always smaller than or equal than the cdf corresponding to the second alternative, then the first alternative is better. This criterion works well in many practical situations, but often, we have situations when for most points, the first cdf is smaller but at some points, the first cdf is larger. In this paper, we show that in such situations of approximate stochastic dominance, we can also conclude that the first alternative is better -- provided that the set of points x at which the first cdf is larger is sufficiently small.