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; Swiss Finance Institute

Freddy Delbaen

Swiss Federal Institute of Technology at Zurich

Samuel Drapeau

CAFR

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

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Freddy Delbaen

Swiss Federal Institute of Technology at Zurich ( email )

ETH-Zentrum
CH-8092 Zurich
Switzerland

Samuel Drapeau

CAFR ( 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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