The Bellman equation for power utility maximization with semimartingales

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.

Published in at http://dx.doi.org/10.1214/11-AAP776 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Cited by in corpus (3)

• A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential Equations
• BSDEs in Utility Maximization with BMO Market Price of Risk
• Power Utility Maximization in Discrete-Time and Continuous-Time Exponential Levy Models