Recursive utility in a Markov environment with stochastic growth

Recursive utility models that feature investor concerns about the intertemporal composition of risk are used extensively in applied research in macroeconomics and asset pricing. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal cond...

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Published inProceedings of the National Academy of Sciences - PNAS Vol. 109; no. 30; pp. 11967 - 11972
Main Authors Hansen, Lars Peter, Scheinkman, José A.
Format Journal Article
LanguageEnglish
Published United States National Academy of Sciences 24.07.2012
National Acad Sciences
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Summary:Recursive utility models that feature investor concerns about the intertemporal composition of risk are used extensively in applied research in macroeconomics and asset pricing. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. 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.
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Author contributions: L.P.H. and J.A.S. designed research, performed research, and wrote the paper.
Edited by David M. Kreps, Stanford University, Stanford, CA, and approved June 7, 2012 (received for review January 6, 2012)
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.1200237109