The Bellman equation for power utility maximization with semimartingales

Details The Bellman equation for power utility maximization with semimartingales The Bellman equation for power utility maximization with semimartingales

2009-12-09

arxiv.org/abs/0912.1883v3

Annals of Applied Probability 2012, Vol. 22, No. 1, 363-406

Economy

Quantitative Finance

Portfolio Management

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

Scientific paper

10.1214/11-AAP776

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.

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