[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/tur/wpapnw/017.html
   My bibliography  Save this paper

Portfolio Optimization over a Finite Horizon with Fixed and Proportional Transaction Costs and Liquidity Constraints

Author

Listed:
  • Stefano Baccarin

    (Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino, Italy)

  • Daniele Marazzina

    (Department of Mathematics, Polytechnic University of Milano, Italy)

Abstract
We investigate a portfolio optimization problem for an agent who invests in two assets, a risk-free and a risky asset modeled by a geometric Brownian motion. The investor faces both fixed and proportional transaction costs and liquidity constraints. His objective is to maximize the expected utility from the portfolio liquidation at a terminal finite horizon. The model is formulated as a parabolic impulse control problem and we characterize the value function as the unique constrained viscosity solution of the associated quasi-variational inequality. We compute numerically the optimal policy by a an iterative finite element discretization technique, presenting extended numerical results in the case of a constant relative risk aversion utility function. Our results show that, even with small transaction costs and distant horizons, the optimal strategy is essentially a buy-and-hold trading strategy where the agent recalibrates his portfolio very few times. This contrasts sharply with the continuous interventions of the Merton's model without transaction costs.

Suggested Citation

  • 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.
    • Handle: RePEc:tur:wpapnw:017
    as

    Download full text from publisher

    File URL: http://www.bemservizi.unito.it/repec/tur/wpapnw/m17.pdf
    File Function: First version, 2013
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Vathana Ly Vath & Mohamed Mnif & Huyên Pham, 2007. "A model of optimal portfolio selection under liquidity risk and price impact," Finance and Stochastics, Springer, vol. 11(1), pages 51-90, January.
    2. 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.
    3. Jerome F. Eastham & Kevin J. Hastings, 1988. "Optimal Impulse Control of Portfolios," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 588-605, November.
    4. Ralf Korn, 1998. "Portfolio optimisation with strictly positive transaction costs and impulse control," Finance and Stochastics, Springer, vol. 2(2), pages 85-114.
    5. Kumar Muthuraman & Sunil Kumar, 2006. "Multidimensional Portfolio Optimization With Proportional Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 301-335, April.
    6. Baccarin, Stefano, 2009. "Optimal impulse control for a multidimensional cash management system with generalized cost functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 198-206, July.
    7. 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.
    8. 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.
    9. Dumas, Bernard & Luciano, Elisa, 1991. "An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-595, June.
    10. 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.
    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. Stefano Baccarin, 2013. "Optimal Consumption of a Generalized Geometric Brownian Motion with Fixed and Variable Intervention Costs," Working papers 021, Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.

    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. Stefano Baccarin & Daniele Marazzina, 2014. "Optimal impulse control of a portfolio with a fixed transaction cost," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(2), pages 355-372, June.
    2. Albert Altarovici & Max Reppen & H. Mete Soner, 2016. "Optimal Consumption and Investment with Fixed and Proportional Transaction Costs," Papers 1610.03958, arXiv.org.
    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. 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.
    6. Albert Altarovici & Johannes Muhle-Karbe & H. Mete Soner, 2013. "Asymptotics for Fixed Transaction Costs," Papers 1306.2802, arXiv.org, revised Oct 2013.
    7. Albert Altarovici & Johannes Muhle-Karbe & Halil Soner, 2015. "Asymptotics for fixed transaction costs," Finance and Stochastics, Springer, vol. 19(2), pages 363-414, April.
    8. 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).
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. repec:hal:wpaper:hal-04086378 is not listed on IDEAS
    15. Chellathurai, Thamayanthi & Draviam, Thangaraj, 2007. "Dynamic portfolio selection with fixed and/or proportional transaction costs using non-singular stochastic optimal control theory," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2168-2195, July.
    16. 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.
    17. Ren Liu & Johannes Muhle-Karbe & Marko H. Weber, 2014. "Rebalancing with Linear and Quadratic Costs," Papers 1402.5306, arXiv.org, revised Sep 2017.
    18. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    19. Nikolay A. Andreev, 2015. "Worst-Case Approach To Strategic Optimal Portfolio Selection Under Transaction Costs And Trading Limits," HSE Working papers WP BRP 45/FE/2015, National Research University Higher School of Economics.
    20. 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.
    21. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.

    More about this item

    Keywords

    Portfolio Optimization; Quasi-variational Inequalities; Transaction Costs; Viscosity Solutions;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:tur:wpapnw:017. 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: Daniele Pennesi (email available below). General contact details of provider: https://edirc.repec.org/data/dstorit.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.