Between First and Second-Order Stochastic Dominance

Management Science 63, 2933–2947

44 Pages Posted: 8 Aug 2015 Last revised: 2 Jan 2018

See all articles by Alfred Müller

Alfred Müller

University of Siegen

Marco Scarsini

LUISS, Dipartimento di Economia e Finanza

Ilia Tsetlin

INSEAD

Robert L. Winkler

Duke University - Fuqua School of Business

Date Written: November 22, 2015

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 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.

Keywords: Stochastic Dominance, Transfers, Indirect Utility

Suggested Citation

Müller, Alfred and Scarsini, Marco and Tsetlin, Ilia and Winkler, Robert L., Between First and Second-Order Stochastic Dominance (November 22, 2015). Management Science 63, 2933–2947. Available at SSRN: https://ssrn.com/abstract=2640879 or http://dx.doi.org/10.2139/ssrn.2640879

Alfred Müller

University of Siegen ( email )

Department Mathematik
Walter-Flex-Str. 3
57068 Siegen
Germany

Marco Scarsini

LUISS, Dipartimento di Economia e Finanza ( email )

Viale Romania 32
Rome, RM 00197
Italy

Ilia Tsetlin (Contact Author)

INSEAD ( email )

Boulevard de Constance
77305 Fontainebleau Cedex
France

Robert L. Winkler

Duke University - Fuqua School of Business ( email )

Box 90120
Durham, NC 27708-0120
United States

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