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Recursive utility in a Markov environment with stochastic growth

Author

Listed:
  • Lars Peter Hansen

    (University of Chicago and NBER)

  • Jose A. Scheinkman

    (Princeton University and NBER)

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.

Suggested Citation

  • Lars Peter Hansen & Jose A. Scheinkman, 2012. "Recursive utility in a Markov environment with stochastic growth," Working Papers 1380, Princeton University, Department of Economics, Econometric Research Program..
  • Handle: RePEc:pri:metric:wp032_hansen-scheinkman-exist.pdf
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    References listed on IDEAS

    as
    1. Lars Peter Hansen & José A. Scheinkman, 2009. "Long-Term Risk: An Operator Approach," Econometrica, Econometric Society, vol. 77(1), pages 177-234, January.
    2. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    3. Stutzer, Michael, 2003. "Portfolio choice with endogenous utility: a large deviations approach," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 365-386.
    4. Kocherlakota, Narayana R., 1990. "On the 'discount' factor in growth economies," Journal of Monetary Economics, Elsevier, vol. 25(1), pages 43-47, January.
    5. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
    6. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-969, July.
    7. Marinacci, Massimo & Montrucchio, Luigi, 2010. "Unique solutions for stochastic recursive utilities," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1776-1804, September.
    8. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
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    Cited by:

    1. Hansen, Lars Peter, 2013. "Risk Pricing over Alternative Investment Horizons," Handbook of the Economics of Finance, Elsevier.
    2. Guo, Jing & He, Xue Dong, 2017. "Equilibrium asset pricing with Epstein-Zin and loss-averse investors," Journal of Economic Dynamics and Control, Elsevier, vol. 76(C), pages 86-108.
    3. Deng, Binbin, 2015. "Regime Learning and Asset Prices in A Long-run Model: Theory," MPRA Paper 79960, University Library of Munich, Germany.

    More about this item

    Keywords

    recursive utility; Markov process; stochastic growth; large deviations;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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