We treat utility maximization from terminal wealth for an agent with utility function U:R\toR 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 in the case where the utility has a "moderate" tail at -\infty . We rely on a recent Koml\'os-type lemma of 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 the cases of frictionless markets with finitely many assets , markets with proportional transaction costs and large financial markets.
We treat utility maximization from terminal wealth for an agent with utility function U:R\toR 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 Koml\'os-type lemma of 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.
D
in the case where the utility has a "moderate" tail at -\infty
D
the cases of
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, markets with proportional transaction costs