A Unified Approach to Portfolio Optimization with Linear Transaction Costs
Bodoe Graduate School of Business Working Paper No. 3/2004
28 Pages Posted: 4 Feb 2010 Last revised: 8 Feb 2010
Date Written: October 6, 2004
In this paper we study the continuous time optimal portfolio selection problem for an investor with a finite horizon who maximizes expected utility of terminal wealth and faces transaction costs in the capital market. It is well known that, depending on a particular structure of transaction costs, such a problem is formulated and solved within either stochastic singular control or stochastic impulse control framework. In this paper we propose a unified framework, which generalizes the contemporary approaches and is capable to deal with any problem where transaction costs are a linear/piecewise-linear function of the volume of trade. We also discuss some methods for solving numerically the problem within our unified framework.
Keywords: portfolio choice, transaction costs, stochastic singular control, stochastic impulse control, computational methods
JEL Classification: C61, C63, G11
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