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

By Alexander Schied. 2012

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Abstract Assuming geometric Brownian motion as unaffected price process , Gatheral and Schied (2011; Optimal trade execution under geometric Brownian motion in the Almgren and Chriss framework, International Journal of Theoretical and Applied Finance, 14, pp. 353–368) 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 . We prove the surprising result that the strategy remains optimal whenever is a square-integrable martingale. We then analyse the optimization criterion of Gatheral and Schied (2011) in the case in which 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.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/dba5aa3da2e43cd6f186c09f60d3ffcbdfaf10c6

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