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Optimal Trade Execution in Illiquid Markets

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  • Erhan Bayraktar
  • Mike Ludkovski

Abstract

We study optimal trade execution strategies in financial markets with discrete order flow. The agent has a finite liquidation horizon and must minimize price impact given a random number of incoming trade counterparties. Assuming that the order flow $N$ is given by a Poisson process, we give a full analysis of the properties and computation of the optimal dynamic execution strategy. Extensions, whereby (a) $N$ is a fully-observed regime-switching Poisson process; and (b) $N$ is a Markov-modulated compound Poisson process driven by a hidden Markov chain, are also considered. We derive and compare the properties of the three cases and illustrate our results with computational examples.

Suggested Citation

  • Erhan Bayraktar & Mike Ludkovski, 2009. "Optimal Trade Execution in Illiquid Markets," Papers 0902.2516, arXiv.org.
    • Handle: RePEc:arx:papers:0902.2516
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    Cited by:

    1. Campi, Luciano & Zabaljauregui, Diego, 2020. "Optimal market making under partial information with general intensities," LSE Research Online Documents on Economics 104612, London School of Economics and Political Science, LSE Library.
    2. Erhan Bayraktar & Michael Ludkovski, 2014. "Liquidation In Limit Order Books With Controlled Intensity," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 627-650, October.
    3. Katia Colaneri & Zehra Eksi & Rudiger Frey & Michaela Szolgyenyi, 2016. "Optimal Liquidation under Partial Information with Price Impact," Papers 1606.05079, arXiv.org, revised Jun 2019.
    4. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    5. Kyle Bechler & Mike Ludkovski, 2014. "Optimal Execution with Dynamic Order Flow Imbalance," Papers 1409.2618, arXiv.org, revised Oct 2014.
    6. Roman Gayduk & Sergey Nadtochiy, 2016. "Endogenous Formation of Limit Order Books: Dynamics Between Trades," Papers 1605.09720, arXiv.org, revised Jun 2017.
    7. Álvaro Cartea & Sebastian Jaimungal & Damir Kinzebulatov, 2016. "Algorithmic Trading With Learning," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-30, June.
    8. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    9. Aur'elien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Papers 1404.0648, arXiv.org, revised Jun 2015.
    10. Clarence Simard & Bruno Rémillard, 2019. "Pricing European Options in a Discrete Time Model for the Limit Order Book," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 985-1005, September.
    11. Roman Gayduk & Sergey Nadtochiy, 2015. "Liquidity Effects of Trading Frequency," Papers 1508.07914, arXiv.org, revised May 2017.
    12. Salvatore Federico & Paul Gassiat & Fausto Gozzi, 2017. "Impact Of Time Illiquidity In A Mixed Market Without Full Observation," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 401-437, April.
    13. Diego Zabaljauregui, 2020. "Optimal market making under partial information and numerical methods for impulse control games with applications," Papers 2009.06521, arXiv.org.
    14. Gerry Tsoukalas & Jiang Wang & Kay Giesecke, 2019. "Dynamic Portfolio Execution," Management Science, INFORMS, vol. 67(5), pages 2015-2040, May.
    15. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Post-Print hal-00971369, HAL.

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