IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2402.14100.html
   My bibliography  Save this paper

A Note on Optimal Liquidation with Linear Price Impact

Author

Listed:
  • Yan Dolinsky
  • Doron Greenstein

Abstract

In this note we consider the maximization of the expected terminal wealth for the setup of quadratic transaction costs. First, we provide a very simple probabilistic solution to the problem. Although the problem was largely studied, as far as we know up to date this simple and probabilistic form of the solution has not appeared in the literature. Next, we apply the general result for the study of the case where the risky asset is given by a fractional Brownian Motion and the information flow of the investor can be diversified.

Suggested Citation

  • Yan Dolinsky & Doron Greenstein, 2024. "A Note on Optimal Liquidation with Linear Price Impact," Papers 2402.14100, arXiv.org.
    • Handle: RePEc:arx:papers:2402.14100
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2402.14100
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Paolo Guasoni & Mikl'os R'asonyi, 2015. "Hedging, arbitrage and optimality with superlinear frictions," Papers 1506.05895, arXiv.org.
    2. Antje Fruth & Torsten Schöneborn & Mikhail Urusov, 2019. "Optimal trade execution in order books with stochastic liquidity," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 507-541, April.
    3. 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.
    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. Yan Dolinsky, 2022. "Duality Theory for Exponential Utility--Based Hedging in the Almgren--Chriss Model," Papers 2210.03917, arXiv.org, revised Jun 2023.
    2. David Evangelista & Yuri Thamsten, 2023. "Approximately optimal trade execution strategies under fast mean-reversion," Papers 2307.07024, arXiv.org, revised Aug 2023.
    3. Leonid Dolinskyi & Yan Dolinsky, 2023. "Optimal Liquidation with High Risk Aversion and Small Linear Price Impact," Papers 2301.01555, arXiv.org, revised Nov 2023.
    4. Ulrich Horst & Xiaonyu Xia, 2019. "Multi-dimensional optimal trade execution under stochastic resilience," Finance and Stochastics, Springer, vol. 23(4), pages 889-923, October.
    5. 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.
    6. Eyal Neuman & Alexander Schied, 2018. "Protecting Pegged Currency Markets from Speculative Investors," Papers 1801.07784, arXiv.org, revised Feb 2021.
    7. Xiaoyue Li & John M. Mulvey, 2023. "Optimal Portfolio Execution in a Regime-switching Market with Non-linear Impact Costs: Combining Dynamic Program and Neural Network," Papers 2306.08809, arXiv.org.
    8. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    9. Claudio Bellani & Damiano Brigo, 2021. "Mechanics of good trade execution in the framework of linear temporary market impact," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 143-163, January.
    10. Fengpei Li & Vitalii Ihnatiuk & Ryan Kinnear & Anderson Schneider & Yuriy Nevmyvaka, 2022. "Do price trajectory data increase the efficiency of market impact estimation?," Papers 2205.13423, arXiv.org, revised Mar 2023.
    11. 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.
    12. Paolo Guasoni & Marko H. Weber, 2018. "Rebalancing Multiple Assets with Mutual Price Impact," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 618-653, November.
    13. Cesari, Riccardo & Marzo, Massimiliano & Zagaglia, Paolo, 2012. "Effective Trade Execution," MPRA Paper 39619, University Library of Munich, Germany.
    14. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2022. "Portfolio liquidation games with self‐exciting order flow," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1020-1065, October.
    15. Damiano Brigo & Giuseppe Di Graziano, 2013. "Optimal execution comparison across risks and dynamics, with solutions for displaced diffusions," Papers 1304.2942, arXiv.org, revised May 2014.
    16. Julien Vaes & Raphael Hauser, 2018. "Optimal Trade Execution with Uncertain Volume Target," Papers 1810.11454, arXiv.org, revised Sep 2021.
    17. 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.
    18. Diasakos, Theodoros M, 2013. "Comparative Statics of Asset Prices: the effect of other assets' risk," SIRE Discussion Papers 2013-94, Scottish Institute for Research in Economics (SIRE).
    19. Yan Dolinsky & Shir Moshe, 2021. "Utility Indifference Pricing with High Risk Aversion and Small Linear Price Impact," Papers 2111.00451, arXiv.org, revised Jan 2022.
    20. Felix Dammann & Giorgio Ferrari, 2023. "Optimal execution with multiplicative price impact and incomplete information on the return," Finance and Stochastics, Springer, vol. 27(3), pages 713-768, July.

    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:2402.14100. 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.