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We study utility maximization for power utility random fields with andwithout intermediate consumption in a general semimartingale model with closedportfolio constraints. We show that any optimal strategy leads to a solution ofthe corresponding Bellman equation. The optimal strategies are describedpointwise in terms of the opportunity process, which is characterized as theminimal solution of the Bellman equation. We also give verification theoremsfor this equation.

The Bellman equation for power utility maximization with semimartingales