The Annals of Applied Probability

The Bellman equation for power utility maximization with semimartingales

Marcel Nutz

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We study utility maximization for power utility random fields with and without intermediate consumption in a general semimartingale model with closed portfolio constraints. We show that any optimal strategy leads to a solution of the corresponding Bellman equation. The optimal strategies are described pointwise in terms of the opportunity process, which is characterized as the minimal solution of the Bellman equation. We also give verification theorems for this equation.

Article information

Ann. Appl. Probab., Volume 22, Number 1 (2012), 363-406.

First available in Project Euclid: 7 February 2012

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Zentralblatt MATH identifier

Primary: 91B28
Secondary: 93E20: Optimal stochastic control 60G44: Martingales with continuous parameter

Power utility Bellman equation opportunity process semimartingale characteristics BSDE


Nutz, Marcel. The Bellman equation for power utility maximization with semimartingales. Ann. Appl. Probab. 22 (2012), no. 1, 363--406. doi:10.1214/11-AAP776.

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