On the Recoverability of Preferences and Beliefs

Posted: 16 May 2000

See all articles by Domenico Cuoco

Domenico Cuoco

University of Pennsylvania - Finance Department

Fernando Zapatero

Questrom School of Business, Boston University

Abstract

We examine the extent to which an investor's tastes and beliefs can be jointly recovered from knowledge of his/her consumption choice. More precisely, we assume that the investor's preferences admit an expected utility representation, but with subjective (unknown) probabilities, and investigate what joint restrictions can be placed on utility functions and beliefs. If the investor draws utility from intertemporal consumption, we show that the set of utility functions and beliefs that are consistent with a given consumption choice can be characterized by a martingale condition. In the Markovian case, this characterization can be restated in terms of a Riccati differential equation that must be satisfied by the investor's relative risk aversion function. To each solution of this differential equation is associated a unique utility function and a unique set of beliefs supporting the given consumption choice. Moreover, we show that the differential equation has at most one solution in the class of utility functions displaying infinite absolute risk aversion at the origin. Thus, preferences (and associated beliefs) can be uniquely recovered within this class.

JEL Classification: G12

Suggested Citation

Cuoco, Domenico and Zapatero, Fernando, On the Recoverability of Preferences and Beliefs. Review of Financial Studies, Vol. 13, No. 2. Available at SSRN: https://ssrn.com/abstract=197654

Domenico Cuoco

University of Pennsylvania - Finance Department ( email )

The Wharton School
3620 Locust Walk
Philadelphia, PA 19104
United States

Fernando Zapatero (Contact Author)

Questrom School of Business, Boston University ( email )

595 Commonwealth Avenue
Boston, MA 02215
United States
617-353-3631 (Phone)

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