Between First- and Second-Order Stochastic Dominance
Alfred Müller, Marco Scarsini, Ilia Tsetlin, Robert L. Winkler
Management Science · 2017 · Volume 63 · Issue 9
Abstract
We develop a continuum of stochastic dominance rules, covering preferences from first- to second-order stochastic dominance. The motivation for such a continuum is that while decision makers have a preference for “more is better,” they are mostly risk averse but cannot assert that they would dislike any risk. For example, situations with targets, aspiration levels, and local convexities in induced utility functions in sequential decision problems may lead to preferences for some risks. We relate our continuum of stochastic dominance rules to utility classes, the corresponding integral conditions, and probability transfers and discuss the usefulness of these interpretations. Several examples involving, e.g., finite-crossing cumulative distribution functions, location-scale families, and induced utility, illustrate the implementation of the framework developed here. Finally, we extend our results to a combined order including convex (risk-taking) stochastic dominance. This paper was accepted by Manel Baucells, decision analysis .
Keywords
(1 + γ) stochastic dominance, transfers, indirect utility
Enable JavaScript for citation tools and additional paper interactions.