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

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

2012-04-12

arxiv.org/abs/1204.2717v2

Economy

Quantitative Finance

Trading and Market Microstructure

Scientific paper

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.

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