The Opportunity Process for Optimal Consumption and Investment with Power Utility

Abstract

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.

24 pages, forthcoming in 'Mathematics and Financial Economics'

References in corpus (3)

• On the Structure of General Mean-Variance Hedging Strategies
• A filtered version of the bipolar theorem of Brannath and Schachermayer
• Risk Aversion Asymptotics for Power Utility Maximization

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