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Optimal Consumption Choice under Uncertainty with Intertemporal Substitution

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Author Info

  • 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.

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File URL: http://128.118.178.162/eps/ge/papers/9908/9908002.pdf
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Bibliographic Info

Paper provided by EconWPA in its series GE, Growth, Math methods with number 9908002.

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Length: 33 pages
Date of creation: 09 Aug 1999
Date of revision:
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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Web page: http://128.118.178.162

Related research

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

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References

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  1. 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.
  2. 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.
  3. Föllmer, Hans & Kabanov, Jurij M., 1997. "Optional decomposition and lagrange multipliers," SFB 373 Discussion Papers 1997,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  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. 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.
  6. G. Constantinides, 1990. "Habit formation: a resolution of the equity premium puzzle," Levine's Working Paper Archive 1397, David K. Levine.
  7. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
  8. repec:wop:humbsf:1998-108 is not listed on IDEAS
  9. 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.
  10. repec:wop:humbsf:1997-31 is not listed on IDEAS
  11. 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.
  12. 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.
  13. 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.
  14. 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. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.

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