The Opportunity Process for Optimal Consumption and Investment with Power Utility

Details The Opportunity Process for Optimal Consumption and Investment with Power Utility The Opportunity Process for Optimal Consumption and Investment with Power Utility

2009-12-09

arxiv.org/abs/0912.1879v2

Math. Financ. Econ., 3(3):139-159, 2010

Economy

Quantitative Finance

Portfolio Management

24 pages, forthcoming in 'Mathematics and Financial Economics'

Scientific paper

10.1007/s11579-010-0031-0

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.

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