We treat utility maximization from terminal wealth for an agent dynamically investing 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.
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