Stochastic Order-Monotone Uncertainty-Averse Preferences

23 Pages Posted: 4 Mar 2015 Last revised: 27 Aug 2015

See all articles by Patrick Cheridito

Patrick Cheridito

ETH Zurich

Freddy Delbaen

Swiss Federal Institute of Technology at Zurich

Samuel Drapeau

China Academy of Financial Research (SAIF) and School of Mathematical Sciences

Michael Kupper

Humboldt University of Berlin - Department of Mathematics

Date Written: August 2015

Abstract

In this paper we derive a numerical representation for general complete preferences respecting the following two principles: a) more is better than less, b) averages are better than extremes. To be able to distinguish between risk and ambiguity we work in an Anscombe-Aumann framework. Our main result is a quasi-concave numerical representation for a class of preferences wide enough to accommodate Ellsberg- as well as Allais-type behavior. Instead of assuming the usual monotonicity we suppose that our preferences are monotone with respect to first order stochastic dominance. Preference for averages expresses uncertainty-aversion. We do not make independence assumptions of any form. In general, our preferences intertwine attitudes towards risk and ambiguity. But if one assumes a weak form of Savage's sure thing principle, there is separation between risk and ambiguity attitudes, and the representation decomposes into state-dependent preference functionals over the consequences and a quasi-concave functional aggregating the preferences of the decision maker in different states of the world.

Keywords: Uncertainty-aversion, stochastic orders, Allais paradox, Ellsberg paradox

JEL Classification: D81

Suggested Citation

Cheridito, Patrick and Delbaen, Freddy and Drapeau, Samuel and Kupper, Michael, Stochastic Order-Monotone Uncertainty-Averse Preferences (August 2015). Available at SSRN: https://ssrn.com/abstract=2572745 or http://dx.doi.org/10.2139/ssrn.2572745

Patrick Cheridito (Contact Author)

ETH Zurich ( email )

Department of Mathematics
8092 Zurich
Switzerland

Freddy Delbaen

Swiss Federal Institute of Technology at Zurich ( email )

ETH-Zentrum
CH-8092 Zurich
Switzerland

Samuel Drapeau

China Academy of Financial Research (SAIF) and School of Mathematical Sciences ( email )

Shanghai Jiao Tong University
211 West Huaihai Road
Shanghai, 200030
China

HOME PAGE: http://www.samuel-drapeau.info

Michael Kupper

Humboldt University of Berlin - Department of Mathematics ( email )

Unter den Linden
Berlin, D-10099
Germany

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