Maximizing the Growth Rate of a Portfolio with Fixed and Proportional Transaction Costs

Maximizing the Growth Rate of a Portfolio with Fixed and Proportional Transaction Costs In this paper a portfolio optimization problem with transaction costs is studied. Transactions of assets are formulated as an impulsive control, which does not allow continuous transactions. The introduction of fixed rate costs has the effect of preventing continuous transactions. The objective of this paper is studying the problem of maximizing the growth rate of expected log utility. A quasi-variational inequality (QVI) of "ergodic type" is derived from the optimization problem. To solve the inequality, we use a perturbation method, where we obtain a necessary estimate of solutions of non-ergodic type QVIs by using a stochastic representation of the solutions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Maximizing the Growth Rate of a Portfolio with Fixed and Proportional Transaction Costs

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Publisher
Springer-Verlag
Copyright
Copyright © 2006 by Springer
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-006-0857-2
Publisher site
See Article on Publisher Site

Abstract

In this paper a portfolio optimization problem with transaction costs is studied. Transactions of assets are formulated as an impulsive control, which does not allow continuous transactions. The introduction of fixed rate costs has the effect of preventing continuous transactions. The objective of this paper is studying the problem of maximizing the growth rate of expected log utility. A quasi-variational inequality (QVI) of "ergodic type" is derived from the optimization problem. To solve the inequality, we use a perturbation method, where we obtain a necessary estimate of solutions of non-ergodic type QVIs by using a stochastic representation of the solutions.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jun 1, 2006

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