Open Access
August 2001 Optimal consumption choice with intertemporal substitution
Peter Bank, Frank Riedel
Ann. Appl. Probab. 11(3): 750-788 (August 2001). DOI: 10.1214/aoap/1015345348


We analyze the intertemporal utility maximization problem under uncertainty for the preferences proposed by Hindy, Huang and Kreps. 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, we prove an infinite-dimensional version of the Kuhn –Tucker theorem which implies necessary and sufficient conditions for optimality. Using this characterization, we show that optimal plans prescribe consuming just enough to keep the induced level of satisfaction always above some stochastic lower bound. When uncertainty is generated by a Lévy process and agents exhibit constant relative risk aversion, we derive solutions in closed form. Depending on the structure of the underlying stochastics, optimal consumption occurs at rates, in gulps, or in a singular way.


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Peter Bank. Frank Riedel. "Optimal consumption choice with intertemporal substitution." Ann. Appl. Probab. 11 (3) 750 - 788, August 2001.


Published: August 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1022.90045
MathSciNet: MR1865023
Digital Object Identifier: 10.1214/aoap/1015345348

Primary: 90A10
Secondary: 60H30

Keywords: Hindy-Huang-Kreps preferences , intertemporal substitution , intertemporal utility , Lévy processes , singular control problem

Rights: Copyright © 2001 Institute of Mathematical Statistics

Vol.11 • No. 3 • August 2001
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