Drift dependence of optimal trade execution strategies under transient price impact
We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. Our approach uses elements from singular stochastic control, even though the problem is essentially non-Markovian due to the transience of price impact and the lack in Markovian structure of the underlying price process. As a corollary, we give a complete solution to the minimization of a certain cost-risk criterion in our setting.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Erhan Bayraktar & Michael Ludkovski, 2011. "Liquidation in Limit Order Books with Controlled Intensity," Papers 1105.0247, arXiv.org, revised Jan 2012.
- Olivier Gu\'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011.
"Optimal Portfolio Liquidation with Limit Orders,"
1106.3279, arXiv.org, revised Jul 2012.
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