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Maximization of the long-term growth rate for a portfolio with fixed and proportional transaction costs

Part of: Miscellaneous topics in calculus of variations and optimal control Stochastic systems and control

Published online by Cambridge University Press:  01 July 2016

Takashi Tamura
Takashi Tamura*
Affiliation:
Osaka University
*
∗ Postal address: Graduate School of Engineering Science, Osaka University, Toyonaka, 560-8531, Japan. Email address: tamura@sigmath.es.osaka-u.ac.jp
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Abstract

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We study the problem of maximizing the long-run average growth of total wealth for a logarithmic utility function under the existence of fixed and proportional transaction costs. The market model consists of one riskless asset and d risky assets. Impulsive control theory is applied to this problem. We derive a quasivariational inequality (QVI) of ‘ergodic’ type and obtain a weak solution for the inequality. Using this solution, we obtain an optimal investment strategy to achieve the optimal growth.

Keywords

Portfolio optimizationtransaction costquasivariational inequalityimpulsive control

MSC classification

Secondary: 93E20: Optimal stochastic control 49N25: Impulsive optimal control problems

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 3 , September 2008 , pp. 673 - 695
Copyright
Copyright © Applied Probability Trust 2008 

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