Mathematics and Financial Economics

, Volume 3, Issue 3–4, pp 139–159 | Cite as

The opportunity process for optimal consumption and investment with power utility

  • Marcel Nutz


We study the utility maximization problem for power utility random fields in a semimartingale financial market, with and without intermediate consumption. The notion of an opportunity process is introduced as a reduced form of the value process of the resulting stochastic control problem. We show how the opportunity process describes the key objects: optimal strategy, value function, and dual problem. The results are applied to obtain monotonicity properties of the optimal consumption.


Power utility Consumption Semimartingale Dynamic programming Convex duality 

JEL Classification

G11 C61 

Mathematics Subject Classification (2000)

91B28 91B42 93E20 60G44 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsETH ZurichZurichSwitzerland

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