A Smooth Model of Decision Making Under Ambiguity

51 Pages Posted: 12 May 2003

See all articles by Peter Klibanoff

Peter Klibanoff

Northwestern University - Kellogg School of Management

Massimo Marinacci

University of Turin - Department of Statistics and Applied Mathematics

Sujoy Mukerji

Queen Mary University of London; International Centre for Economic Research (ICER)

Date Written: April 2003

Abstract

We propose and axiomatize a model of preferences over acts such that the decision maker evaluates acts according to the expectation (over a set of probability measures) of an increasing transformation of an act's expected utility. This expectation is calculated using a subjective probability over the set of probability measures that the decision maker thinks are relevant given her subjective information. A key feature of our model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective information, and ambiguity attitude, a characteristic of the decision maker's tastes. We show that attitudes towards risk are characterized by the shape of the von Neumann-Morgenstern utility function, as usual, while attitudes towards ambiguity are characterized by the shape of the increasing transformation applied to expected utilities. We show that the negative exponential form of this transformation is the special case of constant ambiguity aversion. Ambiguity itself is defined behaviorally and is shown to be characterized by properties of the subjective set of measures. This characterization of ambiguity is formally related to the definitions of subjective ambiguity advanced by Epstein-Zhang (2001) and Ghirardato-Marinacci (2002). One advantage of this model is that the well-developed machinery for dealing with risk attitudes can be applied as well to ambiguity attitudes. The model is also distinct from many in the literature on ambiguity in that it allows smooth, rather than kinked, indifference curves. This leads to different behavior and improved tractability, while still sharing the main features (e.g., Ellsberg's Paradox, etc.). The Maxmin EU model (e.g., Gilboa and Schmeidler (1989)) with a given set of measures may be seen as an extreme case of our model with infinite ambiguity aversion. Two illustrative applications to portfolio choice are offered.

Keywords: Ambiguity, uncertainty, Knightian uncertainty, ambiguity aversion, uncertainty aversion, Ellsberg's Paradox, portfolio choice

JEL Classification: D80, D81

Suggested Citation

Klibanoff, Peter and Marinacci, Massimo and Mukerji, Sujoy, A Smooth Model of Decision Making Under Ambiguity (April 2003). Available at SSRN: https://ssrn.com/abstract=395600 or http://dx.doi.org/10.2139/ssrn.395600

Peter Klibanoff (Contact Author)

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States
847-491-5153 (Phone)
847-467-1220 (Fax)

Massimo Marinacci

University of Turin - Department of Statistics and Applied Mathematics ( email )

Piazza Arbarello 8
Turin, I-10122
Italy

HOME PAGE: http://web.econ.unito.it/gma/massimo.htm

Sujoy Mukerji

Queen Mary University of London ( email )

Mile End
Mile End Road
London, London E1 4NS
United Kingdom

International Centre for Economic Research (ICER)

Villa Gualino
Viale Settimio Severo, 63
10133 Torino
Italy

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
781
Abstract Views
6,626
rank
47,214
PlumX Metrics