The Annals of Applied Probability

Optimal consumption choice with intertemporal substitution

Peter Bank and Frank Riedel

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Abstract

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.

Article information

Source
Ann. Appl. Probab. Volume 11, Number 3 (2001), 750-788.

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1015345348

Digital Object Identifier
doi:10.1214/aoap/1015345348

Mathematical Reviews number (MathSciNet)
MR1865023

Zentralblatt MATH identifier
1022.90045

Subjects
Primary: 90A10
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)

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

Citation

Bank, Peter; Riedel, Frank. Optimal consumption choice with intertemporal substitution. Ann. Appl. Probab. 11 (2001), no. 3, 750--788. doi:10.1214/aoap/1015345348. http://projecteuclid.org/euclid.aoap/1015345348.


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