Robust Strategies for Optimal Order Execution in the Almgren-Chriss Framework
AbstractAssuming 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1204.2717.
Date of creation: Apr 2012
Date of revision: May 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-04-23 (All new papers)
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- 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.
- Christopher Lorenz & Alexander Schied, 2013. "Drift dependence of optimal trade execution strategies under transient price impact," Finance and Stochastics, Springer, Springer, vol. 17(4), pages 743-770, October.
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