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Optimal consumption for recursive preferences with local substitution — the case of certainty

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  • Li, Hanwu
  • Riedel, Frank
  • Yang, Shuzhen

Abstract

We characterize optimal consumption policies in a recursive intertemporal utility framework with local substitution. We establish existence, uniqueness, and a version of the Kuhn–Tucker theorem. The structure of optimal consumption plans is described explicitly for a large class of aggregators. For Epstein-Zin preferences, the solution coincides with the solution of the corresponding time-additive preferences.

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  • Li, Hanwu & Riedel, Frank & Yang, Shuzhen, 2024. "Optimal consumption for recursive preferences with local substitution — the case of certainty," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    • Handle: RePEc:eee:mateco:v:110:y:2024:i:c:s0304406823001258
    DOI: 10.1016/j.jmateco.2023.102932
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    1. Jesus Fernández-Villaverde & Dirk Krueger, 2007. "Consumption over the Life Cycle: Facts from Consumer Expenditure Survey Data," The Review of Economics and Statistics, MIT Press, vol. 89(3), pages 552-565, August.
    2. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    3. Hindy, Ayman & Huang, Chi-fu & Kreps, David, 1992. "On intertemporal preferences in continuous time : The case of certainty," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 401-440.
    4. Philippe Weil, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(1), pages 29-42.
    5. Kristin Reikvam & Fred Espen Benth & Kenneth Hvistendahl Karlsen, 2001. "Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraint: A viscosity solution approach," Finance and Stochastics, Springer, vol. 5(3), pages 275-303.
    6. 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..
    7. Costis Skiadas, 1998. "Recursive utility and preferences for information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(2), pages 293-312.
    8. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    9. Svensson, Lars E. O., 1989. "Portfolio choice with non-expected utility in continuous time," Economics Letters, Elsevier, vol. 30(4), pages 313-317, October.
    10. Anis Matoussi & Hao Xing, 2018. "Convex duality for Epstein–Zin stochastic differential utility," Mathematical Finance, Wiley Blackwell, vol. 28(4), pages 991-1019, October.
    11. Holger Kraft & Thomas Seiferling & Frank Thomas Seifried, 2017. "Optimal consumption and investment with Epstein–Zin recursive utility," Finance and Stochastics, Springer, vol. 21(1), pages 187-226, January.
    12. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    13. Holger Kraft & Frank Seifried & Mogens Steffensen, 2013. "Consumption-portfolio optimization with recursive utility in incomplete markets," Finance and Stochastics, Springer, vol. 17(1), pages 161-196, January.
    14. Schroder, Mark & Skiadas, Costis, 2003. "Optimal lifetime consumption-portfolio strategies under trading constraints and generalized recursive preferences," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 155-202, December.
    15. Duffie, Darrell & Skiadas, Costis, 1994. "Continuous-time security pricing : A utility gradient approach," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 107-131, March.
    16. Bank, Peter & Riedel, Frank, 2000. "Non-time additive utility optimization--the case of certainty," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 271-290, April.
    17. Kristin Reikvam & Fred Espen Benth & Kenneth Hvistendahl Karlsen, 2001. "Optimal portfolio management rules in a non-Gaussian market with durability and intertemporal substitution," Finance and Stochastics, Springer, vol. 5(4), pages 447-467.
    18. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    19. Schroder, Mark & Skiadas, Costis, 1999. "Optimal Consumption and Portfolio Selection with Stochastic Differential Utility," Journal of Economic Theory, Elsevier, vol. 89(1), pages 68-126, November.
    20. Matoussi, Anis & Xing, Hao, 2018. "Convex duality for Epstein-Zin stochastic differential utility," LSE Research Online Documents on Economics 82519, London School of Economics and Political Science, LSE Library.
    21. Hindy, Ayman & Huang, Chi-fu, 1992. "Intertemporal Preferences for Uncertain Consumption: A Continuous Time Approach," Econometrica, Econometric Society, vol. 60(4), pages 781-801, July.
    22. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(2), pages 155-161.
    23. 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.
    24. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    25. Epstein, Larry G, 1987. "The Global Stability of Efficient Intertemporal Allocations," Econometrica, Econometric Society, vol. 55(2), pages 329-355, March.
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    Cited by:

    1. Li, Hanwu & Riedel, Frank, 2024. "Optimal Consumption for Recursive Preferences with Local Substitution under Risk," Center for Mathematical Economics Working Papers 693, Center for Mathematical Economics, Bielefeld University.

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