The opportunity process for optimal consumption and investment with power utility |
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Authors: | Marcel Nutz |
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Institution: | 1. Department of Mathematics, ETH Zurich, R?mistrasse 101, 8092, Zurich, Switzerland
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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. |
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