The Annals of Probability

Optimal consumption from investment and random endowment in incomplete semimartingale markets

Ioannis Karatzas and Gordan Žitković

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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.

Article information

Ann. Probab., Volume 31, Number 4 (2003), 1821-1858.

First available in Project Euclid: 12 November 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 91B28 91B70: Stochastic models
Secondary: 60G07: General theory of processes 60G44: Martingales with continuous parameter

Utility maximization random endowment incomplete markets convex duality stochastic processes finitely additive measures


Karatzas, Ioannis; Žitković, Gordan. Optimal consumption from investment and random endowment in incomplete semimartingale markets. Ann. Probab. 31 (2003), no. 4, 1821--1858. doi:10.1214/aop/1068646367.

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