Optimal consumption choice under uncertainty with intertemporal substitution

Peter Bank and Frank Riedel

No 1999,71, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

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.

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
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Related works:
Working Paper: Optimal Consumption Choice under Uncertainty with Intertemporal Substitution (1999)
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