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October 2003 Optimal consumption from investment and random endowment in incomplete semimartingale markets
Ioannis Karatzas, Gordan Žitković
Ann. Probab. 31(4): 1821-1858 (October 2003). DOI: 10.1214/aop/1068646367


We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and uniqueness result using techniques from convex duality. The notion of "asymptotic elasticity'' of Kramkov and Schachermayer is extended to the time-dependent case. By imposing no smoothness requirements on the utility function in the temporal argument, we can treat both pure consumption and combined consumption--terminal wealth problems in a common framework. To make the duality approach possible, we provide a detailed characterization of the enlarged dual domain which is reminiscent of the enlargement of $\lone$ to its topological bidual $\linfd$, a space of finitely additive measures. As an application, we treat a constrained Itô process market model, as well as a "totally incomplete'' model.


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Ioannis Karatzas. Gordan Žitković. "Optimal consumption from investment and random endowment in incomplete semimartingale markets." Ann. Probab. 31 (4) 1821 - 1858, October 2003.


Published: October 2003
First available in Project Euclid: 12 November 2003

zbMATH: 1076.91017
MathSciNet: MR2016601
Digital Object Identifier: 10.1214/aop/1068646367

Primary: 91B28 , 91B70
Secondary: 60G07 , 60G44

Keywords: convex duality , finitely additive measures , incomplete markets , random endowment , Stochastic processes , utility maximization

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 4 • October 2003
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