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Dynamic optimal execution in a mixed-market-impact Hawkes price model

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  • Aurélien Alfonsi

    ()
    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - Université Paris Est (UPE) - École des Ponts ParisTech (ENPC), INRIA Paris-Rocquencourt - MATHRISK - INRIA - École des Ponts ParisTech (ENPC) - Université Paris-Est Marne-la-Vallée (UPEMLV))

  • Pierre Blanc

    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - Université Paris Est (UPE) - École des Ponts ParisTech (ENPC), INRIA Paris-Rocquencourt - MATHRISK - INRIA - École des Ponts ParisTech (ENPC) - Université Paris-Est Marne-la-Vallée (UPEMLV))

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    Abstract

    We study a linear price impact model including other liquidity takers, whose flow of orders either follows a Poisson or a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-formula optimal strategy describes in particular how one should react to the orders of other traders. This result enables us to discuss the viability of the market. It is shown that Poissonian arrivals of orders lead to quite robust Price Manipulation Strategies in the sense of Huberman and Stanzl. Instead, a particular set of conditions on the Hawkes model balances the self-excitation of the order flow with the resilience of the price, excludes Price Manipulation Strategies and gives some market stability.

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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00971369.

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    Date of creation: 02 Apr 2014
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    Handle: RePEc:hal:wpaper:hal-00971369

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    11. Aurélien Alfonsi & Alexander Schied, 2013. "Capacitary measures for completely monotone kernels via singular control," Post-Print hal-00659421, HAL.
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    16. Stephen Hardiman & Nicolas Bercot & Jean-Philippe Bouchaud, 2013. "Critical reflexivity in financial markets: a Hawkes process analysis," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 86(10), pages 1-9, October.
    17. Aur\'elien Alfonsi & Alexander Schied, 2012. "Capacitary measures for completely monotone kernels via singular control," Papers 1201.2756, arXiv.org, revised Feb 2013.
    18. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
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    20. Aur\'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
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