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On utility maximization without passing by the dual problem

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  • Miklos Rasonyi

Abstract

We treat utility maximization from terminal wealth for an agent with utility function $U:\mathbb{R}\to\mathbb{R}$ who dynamically invests in a continuous-time financial market and receives a possibly unbounded random endowment. We prove the existence of an optimal investment without introducing the associated dual problem. We rely on a recent result of Orlicz space theory, due to Delbaen and Owari which leads to a simple and transparent proof. Our results apply to non-smooth utilities and even strict concavity can be relaxed. We can handle certain random endowments with non-hedgeable risks, complementing earlier papers. Constraints on the terminal wealth can also be incorporated. As examples, we treat frictionless markets with finitely many assets and large financial markets.

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  • Miklos Rasonyi, 2017. "On utility maximization without passing by the dual problem," Papers 1702.00982, arXiv.org, revised Mar 2018.
    • Handle: RePEc:arx:papers:1702.00982
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