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Unique solutions for stochastic recursive utilities

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  • 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.

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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Recursive utilities Koopmans equations Stochastic recursive utilities;

References

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  1. John Y. Campbell, 1995. "Understanding Risk and Return," Harvard Institute of Economic Research Working Papers 1711, Harvard - Institute of Economic Research.
  2. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, vol. 32(1), pages 139-171, February.
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  4. 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).
  5. Ma, Chenghu, 1993. "Market Equilibrium with Heterogenous Recursive-Utility-Maximizing Agents," Economic Theory, Springer, vol. 3(2), pages 243-66, April.
  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 937-69, July.
  7. 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.
  8. Larry G. Epstein & Angelo Melino, 1993. "A Revealed Preference Analysis of Asset Pricing Under Recursive Utility," NBER Working Papers 4524, National Bureau of Economic Research, Inc.
  9. 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.
  10. Juan Rincón-Zapatero & Carlos Rodríguez-Palmero, 2007. "Recursive utility with unbounded aggregators," Economic Theory, Springer, vol. 33(2), pages 381-391, November.
  11. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
  12. 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.
  13. Ma, Chenghu, 1996. "Market Equilibrium with Heterogeneous Recursive-Utility-Maximizing Agents: Corrigendum," Economic Theory, Springer, vol. 7(3), pages 567-70, April.
  14. 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.
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Cited by:
  1. Kraft, Holger & Seifried, Frank Thomas, 2013. "Stochastic differential utility as the continuous-time limit of recursive utility," SAFE Working Paper Series 17, Research Center SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt.
  2. Daniele Pennesi, 2013. "Asset Prices in an Ambiguous Economy," Carlo Alberto Notebooks 315, Collegio Carlo Alberto.
  3. Todd Sarver, 2012. "Optimal Reference Points and Anticipation," Discussion Papers 1566, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Lars Peter Hansen & Jose A. Scheinkman, 2012. "Recursive Utility in a Markov Environment with Stochastic Growth," Working Papers 2012-002, Becker Friedman Institute for Research In Economics.
  5. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Classical Subjective Expected Utility," Working Papers 400, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  6. Jaśkiewicz, Anna & Matkowski, Janusz & Nowak, Andrzej S., 2011. "On Variable Discounting in Dynamic Programming: Applications to Resource Extraction and Other Economic Models," MPRA Paper 31069, University Library of Munich, Germany, revised 24 May 2011.
  7. Eric T. Swanson, 2012. "Risk aversion, risk premia, and the labor margin with generalized recursive preferences," Working Paper Series 2012-17, Federal Reserve Bank of San Francisco.
  8. Gaetano Bloise, 2013. "The structure of competitive equilibrium with unsecured debt," Departmental Working Papers of Economics - University 'Roma Tre' 0187, Department of Economics - University Roma Tre.

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