Friday, August 7, 2015

Between First and Second-Order Stochastic Dominance

MUELLER Alfred, SCARSINI Marco, TSETLIN Ilia, WINKLER Robert L.
Read the working paper
INSEAD Working Paper 2015/55/DSC

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 first-order stochastic dominance often might not be able to rank the distributions, while second-order stochastic dominance can be too restrictive, leaving out decision makers who are mostly risk averse but find some risks attractive. 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 convex (risk-taking) stochastic dominance.