Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-23T02:25:27.906Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

Akian, M., Sulem, A. and Taksar, M. I. (2001). Dynamic optimization of long-term growth rate for a portfolio with transaction costs and logarithmic utility. Math. Finance 11, 153–188.Google Scholar
Bensoussan, A. (1982). Stochastic Control by Functional Analysis Methods (Studies Math. Appl. 12). North-Holland, Amsterdam.Google Scholar
Bensoussan, A. and Lions, J.-L. (1982). Applications of Variational Inequalities in Stochastic Control (Studies Math. Appl. 12). North-Holland, Amsterdam.Google Scholar
Bensoussan, A. and Lions, J.-L. (1984). Impulse Control and Quasivariational Inequalities. Gauthier-Villars, Montrouge.Google Scholar
Bielecki, T. R. and Pliska, S. R. (2000). Risk sensitive asset management with transaction costs. Finance Stoch. 4, 1–33.Google Scholar
Davis, M. H. A. and Norman, A. R. (1990). Portfolio selection with transaction costs. Math. Operat. Res. 15, 676–713.Google Scholar
Duffie, D. and Sun, T. S. (1990). Trans. costs and portfolio choice in a discrete-continuous-time setting. J. Econom. Dynamics Control 14, 35–51.CrossRefGoogle Scholar
Irle, A. and Sass, J. (2006). Optimal portfolio policies under fixed and proportional transaction costs. Adv. Appl. Prob. 38, 916–942.Google Scholar
Merton, R. C. (1969). Lifetime portfolio selection under uncertainty: the continuous-time case. Rev. Econom. Statist. 51, 247–257.Google Scholar
Merton, R. C. (1971). Optimum consumption and portfolio rules in a continuous-time model. J. Econom. Theory 3, 373–413.Google Scholar
Morton, A. and Pliska, S. R. (1995). Optimal portfolio management with fixed transaction costs. Math. Finance 5, 337–356.Google Scholar
Nagai, H. (2004). Risky fraction processes and problems with transaction costs. In Stochastic Processes and Applications to Mathematical Finance, eds Akahori, J. et al., World Scientific, River Edge, NJ, pp. 271–288.Google Scholar
Robin, M. (1981). On some impulse control problems with long run average cost. SIAM J. Control Optimization 19, 333–358.Google Scholar
Robin, M. (1983). Asymptotics in quasivariational inequalities and ergodic control problems. Systems Control Lett. 3, 171–176.Google Scholar
Taksar, M., Klass, M. J. and Assaf, D. (1988). A diffusion model for optimal portfolio selection in the presence of brokerage fees. Math. Operat. Res. 13, 277–294.Google Scholar
Tamura, T. (2006). Maximizing the growth rate of a portfolio with fixed and proportional transaction costs. Appl. Math. Optimization 54, 95–116.Google Scholar