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Optimal Consumption Choice under Uncertainty with Intertemporal Substitution

Author

Listed:
  • Peter Bank

    (Humboldt University Berlin)

  • Frank Riedel

    (Humboldt University Berlin)

Abstract

This abstract will be reformatted upon submission. You don't need to format for line-breaks here!!!!! We extend the analysis of the intertemporal utility maximization problem for Hindy-Huang-Kreps utilities reported in Bank/Riedel(1999) to the stochastic case. Existence and uniqueness of optimal consumption plans are established under arbitrary convex portfolio constraints, including the cases of both complete and incomplete markets. For the complete market setting, Kuhn-Tucker-like necessary and sufficient conditions for optimality are given. Using this characterization, we show that optimal consumption plans are obtained by reflecting the associated level of satisfaction on a stochastic lower bound. When uncertainty is generated by a L{\'e}vy process and agents exhibit constant relative risk aversion, closed-form solutions are derived. Depending on the structure of the underlying stochastics, optimal consumption occurs at rates, in gulps, or singular to Lebesgue measure.

Suggested Citation

  • Peter Bank & Frank Riedel, 1999. "Optimal Consumption Choice under Uncertainty with Intertemporal Substitution," GE, Growth, Math methods 9908002, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpge:9908002
    Note: Type of Document - LATEX; prepared on IBM PC - PC-TEX; to print on PDF; pages: 33; figures: 1
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/ge/papers/9908/9908002.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Sundaresan, Suresh M, 1989. "Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth," Review of Financial Studies, Society for Financial Studies, vol. 2(1), pages 73-89.
    4. 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.
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    7. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    8. H. Föllmer & Y.M. Kabanov, 1997. "Optional decomposition and Lagrange multipliers," Finance and Stochastics, Springer, vol. 2(1), pages 69-81.
    9. 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.
    10. Föllmer, Hans & Kramkov, D. O., 1997. "Optional decompositions under constraints," SFB 373 Discussion Papers 1997,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    11. Jin, Xing & Deng, Shuhui, 1997. "Existence and uniqueness of optimal consumption and portfolio rules in a continuous-time finance model with habit formation and without short sales," Journal of Mathematical Economics, Elsevier, vol. 28(2), pages 187-205, September.
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    Cited by:

    1. Börner, Stefan & Ragg, Hermann, 2010. "Functional diversification of a protease inhibitor gene in the genus Drosophila and its molecular basis," Center for Mathematical Economics Working Papers 415, Center for Mathematical Economics, Bielefeld University.
    2. Jan-Henrik Steg, 2012. "Irreversible investment in oligopoly," Finance and Stochastics, Springer, vol. 16(2), pages 207-224, April.
    3. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.

    More about this item

    Keywords

    Hindy-Huang-Kreps preferences; non-time additive utility optimization; intertemporal utility; intertemporal substitution;

    JEL classification:

    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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