IDEAS home Printed from https://ideas.repec.org/p/zbw/ifwkwp/1449.html
   My bibliography  Save this paper

A renewal theoretic result in portfolio theory under transaction costs with multiple risky assets

Author

Listed:
  • Irle, Albrecht
  • Prelle, Claas

Abstract

We consider a portfolio optimization problem in a Black-Scholes model with n stocks, in which an investor faces both fixed and proportional transaction costs. The performance of an investment strategy is measured by the average return of the corresponding portfolio over an infinite time horizon. At first, we derive a representation of the portfolio value process, which only depends on the relative fractions of the total portfolio value that the investor holds in the different stocks. This representation allows us to consider these so-called risky fractions as the decision variables of the investor. We show a certain kind of stationarity (Harris recurrence) for a quite flexible class of strategies (constant boundary strategies). Then, using renewal theoretic methods, we are able to describe the asymptotic return by the behaviour of the risky fractions in a typical period between two trades. Our results generalize those of [4], who considered a financial market model with one bond and one stock, to a market with a finite number n>1 of stocks.

Suggested Citation

  • Irle, Albrecht & Prelle, Claas, 2008. "A renewal theoretic result in portfolio theory under transaction costs with multiple risky assets," Kiel Working Papers 1449, Kiel Institute for the World Economy (IfW Kiel).
    • Handle: RePEc:zbw:ifwkwp:1449
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/24844/1/579108007.PDF
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Andrew J. Morton & Stanley R. Pliska, 1995. "Optimal Portfolio Management With Fixed Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 337-356, October.
    2. Michael Taksar & Michael J. Klass & David Assaf, 1988. "A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 277-294, May.
    3. Kumar Muthuraman & Sunil Kumar, 2006. "Multidimensional Portfolio Optimization With Proportional Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 301-335, April.
    4. Marianne Akian & Agnès Sulem & Michael I. Taksar, 2001. "Dynamic Optimization of Long‐Term Growth Rate for a Portfolio with Transaction Costs and Logarithmic Utility," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 153-188, April.
    5. 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.
    6. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    7. repec:bla:jfinan:v:59:y:2004:i:1:p:289-338 is not listed on IDEAS
    8. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, vol. 13(2), pages 245-263, October.
    Full references (including those not matched with items on IDEAS)

    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. Irle Albrecht & Prelle Claas, 2009. "A renewal theoretic result in portfolio theory under transaction costs with multiple risky assets," Statistics & Risk Modeling, De Gruyter, vol. 27(3), pages 211-233, December.
    2. Kumar Muthuraman & Haining Zha, 2008. "Simulation‐Based Portfolio Optimization For Large Portfolios With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 115-134, January.
    3. Soren Christensen & Albrecht Irle & Andreas Ludwig, 2016. "Optimal portfolio selection under vanishing fixed transaction costs," Papers 1611.01280, arXiv.org, revised Jul 2017.
    4. Yingting Miao & Qiang Zhang, 2023. "Optimal Investment and Consumption Strategies with General and Linear Transaction Costs under CRRA Utility," Papers 2304.07672, arXiv.org.
    5. Albert Altarovici & Max Reppen & H. Mete Soner, 2016. "Optimal Consumption and Investment with Fixed and Proportional Transaction Costs," Papers 1610.03958, arXiv.org.
    6. 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.
    7. Nabeel Butt, 2019. "On Discrete Probability Approximations for Transaction Cost Problems," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(3), pages 365-389, September.
    8. Muthuraman, Kumar, 2007. "A computational scheme for optimal investment - consumption with proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1132-1159, April.
    9. Thomas Breuer & Martin Jandačka, 2008. "Portfolio selection with transaction costs under expected shortfall constraints," Computational Management Science, Springer, vol. 5(4), pages 305-316, October.
    10. Stefano Baccarin & Daniele Marazzina, 2013. "Portfolio Optimization over a Finite Horizon with Fixed and Proportional Transaction Costs and Liquidity Constraints," Working papers 017, Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
    11. 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.
    12. Jin Hyuk Choi & Tae Ung Gang, 2021. "Optimal investment in illiquid market with search frictions and transaction costs," Papers 2101.09936, arXiv.org, revised Aug 2021.
    13. Soren Christensen & Marc Wittlinger, 2012. "Optimal relaxed portfolio strategies for growth rate maximization problems with transaction costs," Papers 1209.0305, arXiv.org, revised Jun 2013.
    14. Mark Broadie & Weiwei Shen, 2016. "High-Dimensional Portfolio Optimization With Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-49, June.
    15. 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.
    16. Areski Cousin & J'er^ome Lelong & Tom Picard, 2023. "Mean-variance dynamic portfolio allocation with transaction costs: a Wiener chaos expansion approach," Papers 2305.16152, arXiv.org, revised Jun 2023.
    17. Paolo Guasoni & Johannes Muhle-Karbe, 2012. "Portfolio Choice with Transaction Costs: a User's Guide," Papers 1207.7330, arXiv.org.
    18. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2014. "Transaction costs, trading volume, and the liquidity premium," Finance and Stochastics, Springer, vol. 18(1), pages 1-37, January.
    19. Jin Hyuk Choi, 2016. "Optimal consumption and investment with liquid and illiquid assets," Papers 1602.06998, arXiv.org, revised Jan 2019.
    20. Christian Bayer & Bezirgen Veliyev, 2014. "Utility Maximization In A Binomial Model With Transaction Costs: A Duality Approach Based On The Shadow Price Process," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-27.

    More about this item

    Keywords

    Portfolio theory; transaction costs; Harris recurrence; renewal theory;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    Statistics

    Access and download statistics

    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:zbw:ifwkwp:1449. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/iwkiede.html .

    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.