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The opportunity process for optimal consumption and investment with power utility

Nutz, Marcel

In: Mathematics and Financial Economics, 2010, vol. 3, no. 3-4, p. 139-159

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    Title
    • The opportunity process for optimal consumption and investment with power utility
    Author
    • Nutz, Marcel. Department of Mathematics, ETH Zurich, Rämistrasse 101, 8092, Zurich, Switzerland
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:318762
    Summary
    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