On utility maximization without passing by the dual problem

Rásonyi, Miklós (2018) On utility maximization without passing by the dual problem. STOCHASTICS, 90 (4). pp. 1095-1113. ISSN 1744-2508

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Abstract

We treat utility maximization from terminal wealth for an agent with utility function (Formula presented.) 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. © 2018 Informa UK Limited, trading as Taylor & Francis Group

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