Optimal consumption choice under uncertainty with intertemporal substitution
AbstractWe 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. --
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Bibliographic InfoPaper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 1999,71.
Date of creation: 1999
Date of revision:
Hindy-Huang-Kreps preferences; non-time additive utility optimization; intertemporal utility; intertemporal substitution;
Other versions of this item:
- Peter Bank & Frank Riedel, 1999. "Optimal Consumption Choice under Uncertainty with Intertemporal Substitution," GE, Growth, Math methods 9908002, EconWPA.
- D91 - Microeconomics - - Intertemporal Choice - - - Intertemporal Household Choice; Life Cycle Models and Saving
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