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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)

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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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Publisher 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
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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://129.3.20.41

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

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Find related papers by JEL classification:
D91 - Microeconomics - - Intertemporal Choice and Growth - - - Intertemporal Consumer Choice; Life Cycle Models and Saving

References listed on IDEAS
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  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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  4. Peter Bank & Frank Riedel, 1998. "Non-Time Additive Utility Optimization - the Case of Certainty," GE, Growth, Math methods 9811002, EconWPA. [Downloadable!]
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  5. H. Föllmer & D. Kramkov, . "Optional decompositions under constraints," Sonderforschungsbereich 373 1997-31, Humboldt Universitaet Berlin.
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