We treat utility maximization from terminal wealth for an agent dynamically investing}\to in a continuous-time financial market and receiving a possibly unbounded random endowment. The utility function is assumed finite on the whole real line. 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 global strict concavity can be relaxed so we can accommodate, in particular, the problem of minimizing expected loss for a wide class of loss functions . 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 comprising a countably infinite number of assets .
We treat utility maximization from terminal wealth for an agent with utility function U:\mathbb{R}\to\mathbb{R 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 .
R
dynamically investing
with utility function U:\mathbb{R
A
\mathbb{R
R
receiving
receives
D
The utility function is assumed finite on the whole real line.
D
global
D
so we can accommodate, in particular, the problem of minimizing expected loss for a wide class of loss functions
D
comprising a countably infinite number of assets