IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1204.2716.html
   My bibliography  Save this paper

Drift dependence of optimal trade execution strategies under transient price impact

Author

Listed:
  • Christopher Lorenz
  • Alexander Schied

Abstract

We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. Our approach uses elements from singular stochastic control, even though the problem is essentially non-Markovian due to the transience of price impact and the lack in Markovian structure of the underlying price process. As a corollary, we give a complete solution to the minimization of a certain cost-risk criterion in our setting.

Suggested Citation

  • Christopher Lorenz & Alexander Schied, 2012. "Drift dependence of optimal trade execution strategies under transient price impact," Papers 1204.2716, arXiv.org, revised Mar 2013.
    • Handle: RePEc:arx:papers:1204.2716
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1204.2716
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Erhan Bayraktar & Michael Ludkovski, 2014. "Liquidation In Limit Order Books With Controlled Intensity," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 627-650, October.
    2. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    3. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    4. Jim Gatheral & Alexander Schied, 2011. "Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 353-368.
    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. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279, arXiv.org, revised Jul 2012.
    7. repec:dau:papers:123456789/7391 is not listed on IDEAS
    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. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2022. "A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies," Papers 2207.00446, arXiv.org, revised Sep 2023.
    2. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2021. "Self-exciting price impact via negative resilience in stochastic order books," Papers 2112.03789, arXiv.org, revised Jul 2022.
    3. Horst, Ulrich & Xia, Xiaonyu & Zhou, Chao, 2021. "Portfolio Liquidation under Factor Uncertainty," Rationality and Competition Discussion Paper Series 274, CRC TRR 190 Rationality and Competition.
    4. Fayc{c}al Drissi, 2022. "Solvability of Differential Riccati Equations and Applications to Algorithmic Trading with Signals," Papers 2202.07478, arXiv.org, revised Aug 2023.
    5. Eduardo Abi Jaber & Eyal Neuman, 2022. "Optimal Liquidation with Signals: the General Propagator Case," Working Papers hal-03835948, HAL.
    6. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2021. "Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models," Finance and Stochastics, Springer, vol. 25(4), pages 757-810, October.
    7. Roman Gayduk & Sergey Nadtochiy, 2016. "Endogenous Formation of Limit Order Books: Dynamics Between Trades," Papers 1605.09720, arXiv.org, revised Jun 2017.
    8. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2015. "Optimal Asset Liquidation with Multiplicative Transient Price Impact," Papers 1501.01892, arXiv.org, revised Apr 2017.
    9. Eduardo Abi Jaber & Eyal Neuman, 2022. "Optimal Liquidation with Signals: the General Propagator Case," Papers 2211.00447, arXiv.org.
    10. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2016. "Optimal Liquidation under Stochastic Liquidity," Papers 1603.06498, arXiv.org, revised Nov 2017.
    11. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2017. "Stability for gains from large investors' strategies in M1/J1 topologies," Papers 1701.02167, arXiv.org, revised Mar 2018.
    12. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2018. "Optimal liquidation under stochastic liquidity," Finance and Stochastics, Springer, vol. 22(1), pages 39-68, January.
    13. Roman Gayduk & Sergey Nadtochiy, 2015. "Liquidity Effects of Trading Frequency," Papers 1508.07914, arXiv.org, revised May 2017.
    14. Ulrich Horst & Evgueni Kivman, 2021. "Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies," Papers 2103.05957, arXiv.org, revised Jul 2023.
    15. Ulrich Horst & Xiaonyu Xia & Chao Zhou, 2019. "Portfolio liquidation under factor uncertainty," Papers 1909.00748, arXiv.org.
    16. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2022. "Reducing Obizhaeva-Wang type trade execution problems to LQ stochastic control problems," Papers 2206.03772, arXiv.org, revised Sep 2023.
    17. Julien Vaes & Raphael Hauser, 2018. "Optimal Trade Execution with Uncertain Volume Target," Papers 1810.11454, arXiv.org, revised Sep 2021.
    18. Alexander Schied & Elias Strehle & Tao Zhang, 2015. "High-frequency limit of Nash equilibria in a market impact game with transient price impact," Papers 1509.08281, arXiv.org, revised May 2017.
    19. Tao Chen & Mike Ludkovski & Moritz Vo{ss}, 2022. "On Parametric Optimal Execution and Machine Learning Surrogates," Papers 2204.08581, arXiv.org, revised Oct 2023.

    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. Christopher Lorenz & Alexander Schied, 2013. "Drift dependence of optimal trade execution strategies under transient price impact," Finance and Stochastics, Springer, vol. 17(4), pages 743-770, October.
    2. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    3. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    4. Xuefeng Gao & S. J. Deng, 2014. "Hydrodynamic limit of order book dynamics," Papers 1411.7502, arXiv.org, revised Feb 2016.
    5. Jin Ma & Eunjung Noh, 2020. "Equilibrium Model of Limit Order Books: A Mean-field Game View," Papers 2002.12857, arXiv.org, revised Mar 2020.
    6. Saran Ahuja & George Papanicolaou & Weiluo Ren & Tzu-Wei Yang, 2016. "Limit order trading with a mean reverting reference price," Papers 1607.00454, arXiv.org, revised Nov 2016.
    7. S. C. P. Yam & W. Zhou, 2017. "Optimal Liquidation of Child Limit Orders," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 517-545, May.
    8. Aur'elien Alfonsi & Alexander Schied & Florian Klock, 2013. "Multivariate transient price impact and matrix-valued positive definite functions," Papers 1310.4471, arXiv.org, revised Sep 2015.
    9. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    10. Damiano Brigo & Federico Graceffa & Eyal Neuman, 2022. "Price impact on term structure," Quantitative Finance, Taylor & Francis Journals, vol. 22(1), pages 171-195, January.
    11. Rama Cont & Arseniy Kukanov, 2012. "Optimal order placement in limit order markets," Papers 1210.1625, arXiv.org, revised Nov 2014.
    12. Arne Lokka & Junwei Xu, 2020. "Optimal liquidation for a risk averse investor in a one-sided limit order book driven by a Levy process," Papers 2002.03379, arXiv.org, revised Oct 2020.
    13. Alvaro Cartea & Luhui Gan & Sebastian Jaimungal, 2018. "Trading Cointegrated Assets with Price Impact," Papers 1807.01428, arXiv.org.
    14. Alexandre Roch, 2023. "Optimal Liquidation Through a Limit Order Book: A Neural Network and Simulation Approach," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-29, March.
    15. Charles-Albert Lehalle & Charafeddine Mouzouni, 2019. "A Mean Field Game of Portfolio Trading and Its Consequences On Perceived Correlations," Papers 1902.09606, arXiv.org.
    16. Kashyap, Ravi, 2020. "David vs Goliath (You against the Markets), A dynamic programming approach to separate the impact and timing of trading costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    17. 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.
    18. repec:dau:papers:123456789/7391 is not listed on IDEAS
    19. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279, arXiv.org, revised Jul 2012.
    20. Rama Cont & Arseniy Kukanov, 2012. "Optimal order placement in limit order markets," Working Papers hal-00737491, HAL.
    21. Arne Lokka & Junwei Xu, 2020. "Optimal liquidation trajectories for the Almgren-Chriss model with Levy processes," Papers 2002.03376, arXiv.org, revised Sep 2020.

    More about this item

    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:arx:papers:1204.2716. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.