IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v62y2005i2p319-343.html
   My bibliography  Save this article

A unified approach to portfolio optimization with linear transaction costs

Author

Listed:
  • Valeri Zakamouline

Abstract

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. Copyright Springer-Verlag 2005

Suggested Citation

  • Valeri Zakamouline, 2005. "A unified approach to portfolio optimization with linear transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 319-343, November.
    • Handle: RePEc:spr:mathme:v:62:y:2005:i:2:p:319-343
    DOI: 10.1007/s00186-005-0005-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-005-0005-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-005-0005-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ralf Korn, 1999. "Some applications of impulse control in mathematical finance," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 493-518, December.
    2. Phelim Boyle & Xiaodong Lin, 1997. "Optimal Portfolio Selection with Transaction Costs," North American Actuarial Journal, Taylor & Francis Journals, vol. 1(2), pages 27-39.
    3. C. Atkinson & P. Wilmott, 1995. "Portfolio Management With Transaction Costs: An Asymptotic Analysis Of The Morton And Pliska Model," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 357-367, October.
    4. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    5. Clewlow, Les & Hodges, Stewart, 1997. "Optimal delta-hedging under transactions costs," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1353-1376, June.
    6. Andriy Demchuk, 2002. "Portfolio Optimization with Concave Transaction Costs," FAME Research Paper Series rp103, International Center for Financial Asset Management and Engineering.
    7. Ralf Korn, 1998. "Portfolio optimisation with strictly positive transaction costs and impulse control," Finance and Stochastics, Springer, vol. 2(2), pages 85-114.
    8. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
    9. A. E. Whalley & P. Wilmott, 1997. "An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 307-324, July.
    10. Ralf Korn, 2004. "Realism and practicality of transaction cost approaches in continuous-time portfolio optimisation: the scope of the Morton-Pliska approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(2), pages 165-174, October.
    11. Framstad, Nils Chr. & Oksendal, Bernt & Sulem, Agnes, 2001. "Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 233-257, April.
    12. He, Hua, 1990. "Convergence from Discrete- to Continuous-Time Contingent Claims Prices," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 523-546.
    13. Karel Janeček & Steven Shreve, 2004. "Asymptotic analysis for optimal investment and consumption with transaction costs," Finance and Stochastics, Springer, vol. 8(2), pages 181-206, May.
    14. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    15. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    16. Jerome F. Eastham & Kevin J. Hastings, 1988. "Optimal Impulse Control of Portfolios," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 588-605, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Amaro de Matos, João & Silva, Nuno, 2014. "Consuming durable goods when stock markets jump: A strategic asset allocation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 86-104.
    2. Palczewski, Jan & Poulsen, Rolf & Schenk-Hoppé, Klaus Reiner & Wang, Huamao, 2015. "Dynamic portfolio optimization with transaction costs and state-dependent drift," European Journal of Operational Research, Elsevier, vol. 243(3), pages 921-931.
    3. João Amaro de Matos & Nuno Silva, 2012. "Consuming durable goods when stock markets jump: a strategic asset allocation approach," GEMF Working Papers 2012-01, GEMF, Faculty of Economics, University of Coimbra.
    4. Roland Herzog & Karl Kunisch & Jörn Sass, 2013. "Primal-dual methods for the computation of trading regions under proportional transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 101-130, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Valeri Zakamouline, 2004. "A Unified Approach to Portfolio Optimization with Linear Transaction Costs," GE, Growth, Math methods 0404003, University Library of Munich, Germany, revised 28 Apr 2004.
    2. Alev{s} v{C}ern'y & Stephan Denkl & Jan Kallsen, 2013. "Hedging in L\'evy Models and the Time Step Equivalent of Jumps," Papers 1309.7833, arXiv.org, revised Jul 2017.
    3. Johannes Muhle-Karbe & Max Reppen & H. Mete Soner, 2016. "A Primer on Portfolio Choice with Small Transaction Costs," Papers 1612.01302, arXiv.org, revised May 2017.
    4. Albert Altarovici & Max Reppen & H. Mete Soner, 2016. "Optimal Consumption and Investment with Fixed and Proportional Transaction Costs," Papers 1610.03958, arXiv.org.
    5. Yaroslav Melnyk & Frank Thomas Seifried, 2018. "Small†cost asymptotics for long†term growth rates in incomplete markets," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 668-711, April.
    6. Zakamouline, Valeri I., 2006. "European option pricing and hedging with both fixed and proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 30(1), pages 1-25, January.
    7. Albert Altarovici & Johannes Muhle-Karbe & H. Mete Soner, 2013. "Asymptotics for Fixed Transaction Costs," Papers 1306.2802, arXiv.org, revised Oct 2013.
    8. Albert Altarovici & Johannes Muhle-Karbe & Halil Soner, 2015. "Asymptotics for fixed transaction costs," Finance and Stochastics, Springer, vol. 19(2), pages 363-414, April.
    9. Xinfu Chen & Min Dai & Wei Jiang & Cong Qin, 2022. "Asymptotic analysis of long‐term investment with two illiquid and correlated assets," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1133-1169, October.
    10. Valeri Zakamouline, 2003. "European Option Pricing and Hedging with both Fixed and Proportional Transaction Costs," Finance 0311009, University Library of Munich, Germany.
    11. Monoyios, Michael, 2004. "Option pricing with transaction costs using a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 889-913, February.
    12. Maxim Bichuch, 2011. "Pricing a Contingent Claim Liability with Transaction Costs Using Asymptotic Analysis for Optimal Investment," Papers 1112.3012, arXiv.org.
    13. Maxim Bichuch, 2014. "Pricing a contingent claim liability with transaction costs using asymptotic analysis for optimal investment," Finance and Stochastics, Springer, vol. 18(3), pages 651-694, July.
    14. Yingting Miao & Qiang Zhang, 2023. "Optimal Investment and Consumption Strategies with General and Linear Transaction Costs under CRRA Utility," Papers 2304.07672, arXiv.org.
    15. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org, revised May 2015.
    16. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    17. Dai, Min & Wang, Hefei & Yang, Zhou, 2012. "Leverage management in a bull–bear switching market," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1585-1599.
    18. Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2016. "Hedging under an expected loss constraint with small transaction costs," Post-Print hal-00863562, HAL.
    19. repec:dau:papers:123456789/5374 is not listed on IDEAS
    20. Martin Herdegen & Johannes Muhle-Karbe, 2018. "Stability of Radner equilibria with respect to small frictions," Finance and Stochastics, Springer, vol. 22(2), pages 443-502, April.
    21. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:62:y:2005:i:2:p:319-343. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.