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Optimal consumption choice under uncertainty with intertemporal substitution

Author

Listed:
  • Bank, Peter
  • Riedel, Frank
Abstract
We extend the analysis of the intertemporal utility maximization problem for Hindy-Huang-Kreps utilities reported in Bank and Riedel (1998) to the stochastic case. Existence and uniqueness of optimal consumption plans are established under arbitrary convex portfolio constraints, including both complete and incomplete markets. For the complete market setting, Kuhn-Tuckerlike necessary and sufficient conditions for optimality are given. Using this characterization, we show that optimal consumption plans are obtained by re- flecting the associated level of satisfaction on a stochastic lower bound. When uncertainty is generated by a Lévy 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

  • Bank, Peter & Riedel, Frank, 1999. "Optimal consumption choice under uncertainty with intertemporal substitution," SFB 373 Discussion Papers 1999,71, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199971
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    References listed on IDEAS

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    1. 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.
    2. D. Vallière & E. Denis & Y. Kabanov, 2009. "Hedging of American options under transaction costs," Finance and Stochastics, Springer, vol. 13(1), pages 105-119, January.
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    4. 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.
    5. 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.
    6. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    7. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-543, June.
    8. 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.
    9. 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.
    10. Sundaresan, Suresh M, 1989. "Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth," The Review of Financial Studies, Society for Financial Studies, vol. 2(1), pages 73-89.
    11. 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.
    12. 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.
    13. Ralf Korn, 1997. "Optimal Portfolios:Stochastic Models for Optimal Investment and Risk Management in Continuous Time," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 3548, August.
    14. Cuoco, Domenico, 1997. "Optimal Consumption and Equilibrium Prices with Portfolio Constraints and Stochastic Income," Journal of Economic Theory, Elsevier, vol. 72(1), pages 33-73, January.
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    Cited by:

    1. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
    2. Riedel, Frank, 2005. "Generic determinacy of equilibria with local substitution," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 603-616, August.
    3. Jan-Henrik Steg, 2012. "Irreversible investment in oligopoly," Finance and Stochastics, Springer, vol. 16(2), pages 207-224, April.

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    More about this item

    Keywords

    Hindy-Huang-Kreps preferences; non-time additive utility optimization; intertemporal utility; intertemporal substitution;
    All these keywords.

    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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