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arXiv · 0706.0051

Optimal consumption from investment and random endowment in incomplete semimartingale markets

Ioannis Karatzas·Gordan Zitkovic
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Abstract

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 $L^1$ to its topological bidual $(L^{\infty})^*$, a space of finitely-additive measures. As an application, we treat the case of a constrained It\^ o-process market-model.

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Ioannis Karatzas, Gordan Zitkovic. 2007-06-01. Optimal consumption from investment and random endowment in incomplete semimartingale markets. https://arxiv.org/abs/0706.0051

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