Research Publication

July 2012 | Article

Recursive Utility in a Markov Environment with Stochastic Growth

Lars Peter Hansen, Jose A. Sheinkman

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.

Journal: Proceedings of the National Academy of Sciences|Volume: 109|Issue Number: 30|Pages: 11967-11972|Tags: Financial Market Linkages to the Macroeconomy, Uncertainty and Valuation|Export BibTeX >
  title={Recursive Utility in a Markov Environment With Stochastic Growth},
  author={Hansen, Lars Peter and Scheinkman, Jos{'e} A},
  journal={Proceedings of the National Academy of Sciences},
  publisher={National Acad Sciences}