IDEAS home Printed from
   My bibliography  Save this paper

Robust Strategies for Optimal Order Execution in the Almgren-Chriss Framework


  • Alexander Schied


Assuming geometric Brownian motion as unaffected price process $S^0$, Gatheral & Schied (2011) derived a strategy for optimal order execution that reacts in a sensible manner on market changes but can still be computed in closed form. Here we will investigate the robustness of this strategy with respect to misspecification of the law of $S^0$. We prove the surprising result that the strategy remains optimal whenever $S^0$ is a square-integrable martingale. We then analyze the optimization criterion of Gatheral & Schied (2011) in the case in which $S^0$ is any square-integrable semimartingale and we give a closed-form solution to this problem. As a corollary, we find an explicit solution to the problem of minimizing the expected liquidation costs when the unaffected price process is a square-integrable semimartingale. The solutions to our problems are found by stochastically solving a finite-fuel control problem without assumptions of Markovianity.

Suggested Citation

  • Alexander Schied, 2012. "Robust Strategies for Optimal Order Execution in the Almgren-Chriss Framework," Papers 1204.2717,, revised May 2013.
  • Handle: RePEc:arx:papers:1204.2717

    Download full text from publisher

    File URL:
    File Function: Latest version
    Download Restriction: no


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Takashi Kato, 2017. "An Optimal Execution Problem in the Volume-Dependent Almgren-Chriss Model," Papers 1701.08972,, revised Aug 2017.
    2. 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.
    3. Erhan Bayraktar & Alexander Munk, 2017. "Mini-Flash Crashes, Model Risk, and Optimal Execution," Papers 1705.09827,
    4. Phillip Monin, 2014. "Hedging Market Risk in Optimal Liquidation," Working Papers 14-08, Office of Financial Research, US Department of the Treasury.
    5. Álvaro Cartea & Sebastian Jaimungal & Damir Kinzebulatov, 2016. "Algorithmic Trading With Learning," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-30, June.
    6. repec:eee:ejores:v:264:y:2018:i:3:p:1159-1171 is not listed on IDEAS
    7. Damiano Brigo & Giuseppe Di Graziano, 2013. "Optimal execution comparison across risks and dynamics, with solutions for displaced diffusions," Papers 1304.2942,, revised May 2014.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:1204.2717. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.