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Unique solutions for stochastic recursive utilities

Author

Listed:
  • Marinacci, Massimo
  • Montrucchio, Luigi

Abstract

We study unique and globally attracting solutions of a general nonlinear stochastic equation, widely used in Finance and Macroeconomics and closely related to stochastic Koopmans equations. The equation is specified by a temporal aggregator W and a certainty equivalent operator . The main contribution of the paper is the introduction of the new class of Thompson aggregators. Other contributions of the paper are: (i) a detailed analysis of quasi-arithmetic operators that generalize those of Kreps and Porteus (1978) [18]; (ii) a clarification of the nature and properties of the stochastic recursive preferences that underlie Koopmans equations.

Suggested Citation

  • Marinacci, Massimo & Montrucchio, Luigi, 2010. "Unique solutions for stochastic recursive utilities," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1776-1804, September.
    • Handle: RePEc:eee:jetheo:v:145:y:2010:i:5:p:1776-1804
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    References listed on IDEAS

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    1. Le Van, Cuong & Vailakis, Yiannis, 2005. "Recursive utility and optimal growth with bounded or unbounded returns," Journal of Economic Theory, Elsevier, vol. 123(2), pages 187-209, August.
    2. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    3. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
    4. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    5. Larry G. Epstein & Angelo Melino, 1995. "A Revealed Preference Analysis of Asset Pricing Under Recursive Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(4), pages 597-618.
    6. Ozaki, Hiroyuki & Streufert, Peter A., 1996. "Dynamic programming for non-additive stochastic objectives," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 391-442.
    7. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
    8. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, vol. 32(1), pages 139-171, February.
    9. Ma, Chenghu, 1998. "Attitudes toward the timing of resolution of uncertainty and the existence of recursive utility," Journal of Economic Dynamics and Control, Elsevier, vol. 23(1), pages 97-112, September.
    10. Montrucchio, Luigi, 1998. "Thompson metric, contraction property and differentiability of policy functions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 449-466, January.
    11. Ma, Chenghu, 1993. "Market Equilibrium with Heterogenous Recursive-Utility-Maximizing Agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 243-266, April.
    12. 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.
    13. Ma, Chenghu, 1996. "Market Equilibrium with Heterogeneous Recursive-Utility-Maximizing Agents: Corrigendum," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 567-570, April.
    14. Chenghu Ma, 1996. "Market equilibrium with heterogeneous recursive-utility-maximizing agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 567-570.
    15. Cuong Le Van & Yiannis Vailakis, 2005. "Recursive utility and optimal growth with bounded or unbounded returns," Post-Print halshs-00101201, HAL.
    16. Juan Rincón-Zapatero & Carlos Rodríguez-Palmero, 2007. "Recursive utility with unbounded aggregators," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(2), pages 381-391, November.
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