Optimal Consumption Choice under Uncertainty with Intertemporal Substitution

Peter Bank and Frank Riedel ()
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Peter Bank: Humboldt University Berlin

GE, Growth, Math methods from EconWPA

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.

Keywords: Hindy-Huang-Kreps preferences; non-time additive utility optimization; intertemporal utility; intertemporal substitution (search for similar items in EconPapers)
JEL-codes: D91 (search for similar items in EconPapers)
Date: 1999-08-09
Note: Type of Document - LATEX; prepared on IBM PC - PC-TEX; to print on PDF; pages: 33; figures: 1
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Working Paper: Optimal Consumption Choice under Uncertainty with Intertemporal Substitution
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpge:9908002

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