Optimal consumption choice with intertemporal substitution
Peter Bank and Frank Riedel
Source: Ann. Appl. Probab. Volume 11, Number 3
(2001), 750-788.
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.
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Keywords: Hindy-Huang-Kreps preferences; intertemporal utility; intertemporal substitution; singular control problem; Lévy processes
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoap/1015345348
Mathematical Reviews number (MathSciNet): MR1865023
Digital Object Identifier: doi:10.1214/aoap/1015345348
Zentralblatt MATH identifier: 1022.90045
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