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Anticipative portfolio optimization

Part of: Stochastic systems and control Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Igor Pikovsky  and
Ioannis Karatzas
Igor Pikovsky*
Affiliation:
Carnegie Mellon University
Ioannis Karatzas*
Affiliation:
Columbia University
*
∗ Postal address: Department of Mathematics, Carnegie-Mellon University, Pittsburgh, PA 15213, USA. pikovsky@andrew.cmu.edu.
∗∗ Postal address: Departments of Mathematics and Statistics, Columbia University, New York, NY 10027, USA. ik@math.columbia.edu.
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Abstract

We study a classical stochastic control problem arising in financial economics: to maximize expected logarithmic utility from terminal wealth and/or consumption. The novel feature of our work is that the portfolio is allowed to anticipate the future, i.e. the terminal values of the prices, or of the driving Brownian motion, are known to the investor, either exactly or with some uncertainty. Results on the finiteness of the value of the control problem are obtained in various setups, using techniques from the so-called enlargement of filtrations. When the value of the problem is finite, we compute it explicitly and exhibit an optimal portfolio in closed form.

Keywords

OPTIMAL PORTFOLIOSSTOCHASTIC CONTROLSTOCHASTIC ANALYSISENLARGEMENT OF FILTRATIONSRELATIVE ENTROPY

MSC classification

Primary: 93E20: Optimal stochastic control 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 60G44: Martingales with continuous parameter
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 28 , Issue 4 , December 1996 , pp. 1095 - 1122
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

Research supported in part by the National Science Foundation under Grant NSF-DMS-93-19816.

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