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Drift dependence of optimal trade execution strategies under transient price impact

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  • Christopher Lorenz
  • Alexander Schied
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    Abstract

    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.

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    File URL: http://arxiv.org/pdf/1204.2716
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1204.2716.

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    Date of creation: Apr 2012
    Date of revision: Mar 2013
    Handle: RePEc:arx:papers:1204.2716

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    Web page: http://arxiv.org/

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    1. Guéant, Olivier & Lehalle, Charles-Albert & Tapia, Joaquin Fernandez, 2011. "Optimal Portfolio Liquidation with Limit Orders," Economics Papers from University Paris Dauphine 123456789/7391, Paris Dauphine University.
    2. Olivier Gu\'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279, arXiv.org, revised Jul 2012.
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