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Drift dependence of optimal trade execution strategies under transient price impact

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  • Christopher Lorenz

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  • Alexander Schied

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Abstract

We give a complete solution to the problem of minimizing the expected liquidity costs in the 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. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Christopher Lorenz & Alexander Schied, 2013. "Drift dependence of optimal trade execution strategies under transient price impact," Finance and Stochastics, Springer, vol. 17(4), pages 743-770, October.
  • Handle: RePEc:spr:finsto:v:17:y:2013:i:4:p:743-770
    DOI: 10.1007/s00780-013-0211-x
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    File URL: http://hdl.handle.net/10.1007/s00780-013-0211-x
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Roman Gayduk & Sergey Nadtochiy, 2015. "Liquidity Effects of Trading Frequency," Papers 1508.07914, arXiv.org, revised May 2017.
    2. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2015. "Optimal Asset Liquidation with Multiplicative Transient Price Impact," Papers 1501.01892, arXiv.org, revised Apr 2017.
    3. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2016. "Optimal Liquidation under Stochastic Liquidity," Papers 1603.06498, arXiv.org, revised Nov 2017.
    4. Roman Gayduk & Sergey Nadtochiy, 2016. "Endogenous Formation of Limit Order Books: Dynamics Between Trades," Papers 1605.09720, arXiv.org, revised Jun 2017.
    5. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2018. "Optimal liquidation under stochastic liquidity," Finance and Stochastics, Springer, vol. 22(1), pages 39-68, January.
    6. Ulrich Horst & Evgueni Kivman, 2021. "Small impact analysis in stochastically illiquid markets," Papers 2103.05957, arXiv.org.
    7. Ulrich Horst & Xiaonyu Xia & Chao Zhou, 2019. "Portfolio liquidation under factor uncertainty," Papers 1909.00748, arXiv.org.
    8. Alexander Schied & Elias Strehle & Tao Zhang, 2015. "High-frequency limit of Nash equilibria in a market impact game with transient price impact," Papers 1509.08281, arXiv.org, revised May 2017.
    9. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2017. "Stability for gains from large investors' strategies in M1/J1 topologies," Papers 1701.02167, arXiv.org, revised Mar 2018.
    10. Julien Vaes & Raphael Hauser, 2018. "Optimal execution strategy with an uncertain volume target," Papers 1810.11454, arXiv.org, revised May 2020.

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    More about this item

    Keywords

    Optimal trade execution; Optimal order execution; Transient price impact; Singular control; Verification argument; 91G80; 60H30; 49N10; 93E20; C02; C61; G11; G12; G14; G19;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G19 - Financial Economics - - General Financial Markets - - - Other

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