Recursive Utility in a Markov Environment with Stochastic Growth

Posted: 27 Feb 2012

See all articles by José A. Scheinkman

José A. Scheinkman

Columbia University; Princeton University - Department of Economics; National Bureau of Economic Research (NBER)

Lars Peter Hansen

University of Chicago - Department of Economics; National Bureau of Economic Research (NBER)

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Date Written: January 17, 2012

Abstract

Recursive utility models of the type introduced by Kreps and Porteus (1978) are used extensively in applied research in macroeconomics and asset pricing in environments with uncertainty. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. Such preferences feature investor concerns about the intertemporal composition of risk. In this paper we study infinite horizon specifications of this difference equation in the context of a Markov environment. We establish a connection between the solution to this equation and to an arguably simpler Perron-Frobenius eigenvalue equation of the type that occurs in the study of large deviations for Markov processes. By exploiting this connection, we establish existence and uniqueness results. Moreover, we explore a substantive link between large deviation bounds for tail events for stochastic consumption growth and preferences induced by recursive utility.

Keywords: recursive utility, Markov process, stochastic growth, large deviations

Suggested Citation

Scheinkman, José and Hansen, Lars Peter, Recursive Utility in a Markov Environment with Stochastic Growth (January 17, 2012). Available at SSRN: https://ssrn.com/abstract=2011792

José Scheinkman (Contact Author)

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Lars Peter Hansen

University of Chicago - Department of Economics ( email )

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National Bureau of Economic Research (NBER)

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