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Unique solutions for stochastic recursive utilities

  • Marinacci, Massimo
  • Montrucchio, Luigi

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.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 5 (September)
Pages: 1776-1804

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:5:p:1776-1804
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. 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.
  2. Juan Rincón-Zapatero & Carlos Rodríguez-Palmero, 2007. "Recursive utility with unbounded aggregators," Economic Theory, Springer, vol. 33(2), pages 381-391, November.
  3. Ozaki, Hiroyuki & Streufert, Peter A., 1996. "Dynamic programming for non-additive stochastic objectives," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 391-442.
  4. 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 937-69, July.
  5. Epstein, Larry G & Melino, Angelo, 1995. "A Revealed Preference Analysis of Asset Pricing under Recursive Utility," Review of Economic Studies, Wiley Blackwell, vol. 62(4), pages 597-618, October.
  6. 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.
  7. John Y. Campbell, 1993. "Understanding Risk and Return," NBER Working Papers 4554, National Bureau of Economic Research, Inc.
  8. 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 263-86, April.
  9. LE VAN, Cuong & VAILAKIS, Yiannis, 2002. "Recursive utility and optimal growth with bounded or unbounded returns," CORE Discussion Papers 2002055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Ma, Chenghu, 1996. "Market Equilibrium with Heterogeneous Recursive-Utility-Maximizing Agents: Corrigendum," Economic Theory, Springer, vol. 7(3), pages 567-70, April.
  11. Robert E. Lucas Jr. & Nancy L. Stokey, 1982. "Optimal Growth with Many Consumers," Discussion Papers 518, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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, 1993. "Market Equilibrium with Heterogenous Recursive-Utility-Maximizing Agents," Economic Theory, Springer, vol. 3(2), pages 243-66, April.
  14. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
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