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Anticipative portfolio optimization

Published online by Cambridge University Press:  01 July 2016

Igor Pikovsky*
Affiliation:
Carnegie Mellon University
Ioannis Karatzas*
Affiliation:
Columbia University
*
Postal address: Department of Mathematics, Carnegie-Mellon University, Pittsburgh, PA 15213, USA. [email protected].
∗∗ Postal address: Departments of Mathematics and Statistics, Columbia University, New York, NY 10027, USA. [email protected].

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.

Type
General Applied Probability
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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