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

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  • Alexander Schied

Abstract

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, arXiv.org, revised May 2013.
  • Handle: RePEc:arx:papers:1204.2717
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    File URL: http://arxiv.org/pdf/1204.2717
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    Cited by:

    1. Takashi Kato, 2017. "An Optimal Execution Problem in the Volume-Dependent Almgren-Chriss Model," Papers 1701.08972, arXiv.org, 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, arXiv.org.
    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, arXiv.org, revised May 2014.

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