IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v22y2019i07ns0219024919500390.html
   My bibliography  Save this article

Singular Perturbation Expansion For Utility Maximization With Order-𝜖 Quadratic Transaction Costs

Author

Listed:
  • SHIVA CHANDRA

    (Department of Finance and Risk Engineering, NYU Tandon School of Engineering, Brooklyn NY, USA)

  • ANDREW PAPANICOLAOU

    (Department of Finance and Risk Engineering, NYU Tandon School of Engineering, Brooklyn NY, USA)

Abstract

We present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order 𝜖 small, which leads to the optimization problem having an asymptotically-singular Hamilton–Jacobi–Bellman equation whose solution can be expanded in powers of 𝜖. In this paper, we derive explicit formulae for the first two terms of this expansion. Analysis and simulation are provided to show the behavior of this approximating solution.

Suggested Citation

  • Shiva Chandra & Andrew Papanicolaou, 2019. "Singular Perturbation Expansion For Utility Maximization With Order-𝜖 Quadratic Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(07), pages 1-18, November.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:07:n:s0219024919500390
    DOI: 10.1142/S0219024919500390
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024919500390
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024919500390?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. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584, December.
    2. Nicolae Gârleanu & Lasse Heje Pedersen, 2013. "Dynamic Trading with Predictable Returns and Transaction Costs," Journal of Finance, American Finance Association, vol. 68(6), pages 2309-2340, December.
    3. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183, World Scientific Publishing Co. Pte. Ltd..
    4. Jean-Pierre Fouque & George Papanicolaou & K. Ronnie Sircar, 2001. "From The Implied Volatility Skew To A Robust Correction To Black-Scholes American Option Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(04), pages 651-675.
    5. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    6. 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.
    7. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    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. Ren Liu & Johannes Muhle-Karbe & Marko H. Weber, 2014. "Rebalancing with Linear and Quadratic Costs," Papers 1402.5306, arXiv.org, revised Sep 2017.
    2. Koichi Matsumoto, 2007. "Portfolio Insurance with Liquidity Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(4), pages 363-386, December.
    3. Adrian Buss & Bernard Dumas, 2019. "The Dynamic Properties of Financial‐Market Equilibrium with Trading Fees," Journal of Finance, American Finance Association, vol. 74(2), pages 795-844, April.
    4. Etienne Chevalier & Vathana Ly Vath & Simone Scotti & Alexandre Roch, 2016. "Optimal Execution Cost For Liquidation Through A Limit Order Market," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-26, February.
    5. Rim Bernoussi & Michael Rockinger, 2023. "Rebalancing with transaction costs: theory, simulations, and actual data," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 37(2), pages 121-160, June.
    6. Mariani, Francesca & Recchioni, Maria Cristina & Ciommi, Mariateresa, 2019. "Merton’s portfolio problem including market frictions: A closed-form formula supporting the shadow price approach," European Journal of Operational Research, Elsevier, vol. 275(3), pages 1178-1189.
    7. Peter Bank & Ibrahim Ekren & Johannes Muhle‐Karbe, 2021. "Liquidity in competitive dealer markets," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 827-856, July.
    8. Jan Kallsen & Johannes Muhle-Karbe, 2014. "High-Resilience Limits of Block-Shaped Order Books," Papers 1409.7269, arXiv.org.
    9. Maxim Bichuch & Ronnie Sircar, 2014. "Optimal Investment with Transaction Costs and Stochastic Volatility," Papers 1401.0562, arXiv.org, revised Aug 2014.
    10. Qixuan Luo & Yu Shi & Handong Li, 2021. "Research on Portfolio Liquidation Strategy under Discrete Times," Papers 2103.15400, arXiv.org.
    11. Clarence Simard & Bruno Rémillard, 2019. "Pricing European Options in a Discrete Time Model for the Limit Order Book," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 985-1005, September.
    12. Cayé, Thomas & Herdegen, Martin & Muhle-Karbe, Johannes, 2020. "Scaling limits of processes with fast nonlinear mean reversion," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1994-2031.
    13. Alain Bensoussan & Guiyuan Ma & Chi Chung Siu & Sheung Chi Phillip Yam, 2022. "Dynamic mean–variance problem with frictions," Finance and Stochastics, Springer, vol. 26(2), pages 267-300, April.
    14. Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2016. "Hedging under an expected loss constraint with small transaction costs," Post-Print hal-00863562, HAL.
    15. Mei, Xiaoling & Nogales Martín, Francisco Javier, 2015. "Portfolio selection with proportional transaction costs and predictability," DES - Working Papers. Statistics and Econometrics. WS ws1521, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Yaoting Lei & Ya Li & Jing Xu, 2020. "Two Birds, One Stone: Joint Timing of Returns and Capital Gains Taxes," Management Science, INFORMS, vol. 66(2), pages 823-843, February.
    17. 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.
    18. Jorge Guijarro-Ordonez, 2019. "High-dimensional statistical arbitrage with factor models and stochastic control," Papers 1901.09309, arXiv.org, revised Jun 2021.
    19. Felix J. Lopez-Iturriaga & Domingo Javier Santana-Martin, 2015. "Do Shareholder Coalitions Modify Dominant Owner's Control? The Impact On Dividend Policy," HSE Working papers WP BRP 41/FE/2015, National Research University Higher School of Economics.
    20. Masamitsu Ohnishi & Makoto Shimoshimizu, 2022. "Optimal Pair–Trade Execution with Generalized Cross–Impact," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(2), pages 253-289, June.

    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:wsi:ijtafx:v:22:y:2019:i:07:n:s0219024919500390. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.