The Annals of Applied Probability

The Bellman equation for power utility maximization with semimartingales

Marcel Nutz

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Abstract

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

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

Dates
First available in Project Euclid: 7 February 2012

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1328623703

Digital Object Identifier
doi:10.1214/11-AAP776

Mathematical Reviews number (MathSciNet)
MR2932550

Zentralblatt MATH identifier
1239.91165

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

Keywords
Power utility Bellman equation opportunity process semimartingale characteristics BSDE

Citation

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. https://projecteuclid.org/euclid.aoap/1328623703.


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