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Optimal posting price of limit orders: learning by trading

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  • Sophie Laruelle

    (LPMA)

  • Charles-Albert Lehalle

    (LPMA)

  • Gilles Pag`es

    (LPMA)

Abstract

Considering that a trader or a trading algorithm interacting with markets during continuous auctions can be modeled by an iterating procedure adjusting the price at which he posts orders at a given rhythm, this paper proposes a procedure minimizing his costs. We prove the a.s. convergence of the algorithm under assumptions on the cost function and give some practical criteria on model parameters to ensure that the conditions to use the algorithm are fulfilled (using notably the co-monotony principle). We illustrate our results with numerical experiments on both simulated data and using a financial market dataset.

Suggested Citation

  • Sophie Laruelle & Charles-Albert Lehalle & Gilles Pag`es, 2011. "Optimal posting price of limit orders: learning by trading," Papers 1112.2397, arXiv.org, revised Sep 2012.
    • Handle: RePEc:arx:papers:1112.2397
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    References listed on IDEAS

    as
    1. Erhan Bayraktar & Michael Ludkovski, 2014. "Liquidation In Limit Order Books With Controlled Intensity," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 627-650, October.
    2. 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.
    3. Thierry Foucault & Ohad Kadan & Eugene Kandel, 2005. "Limit Order Book as a Market for Liquidity," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1171-1217.
    4. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Dealing with the Inventory Risk. A solution to the market making problem," Papers 1105.3115, arXiv.org, revised Aug 2012.
    5. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    6. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    7. Fabien Guilbaud & Huyen Pham, 2011. "Optimal High Frequency Trading with limit and market orders," Working Papers hal-00603385, HAL.
    8. repec:dau:papers:123456789/7390 is not listed on IDEAS
    9. Fabien Guilbaud & Mohamed Mnif & Huy^en Pham, 2010. "Numerical methods for an optimal order execution problem," Papers 1006.0768, arXiv.org.
    10. Fabien Guilbaud & Huyen Pham, 2011. "Optimal High Frequency Trading with limit and market orders," Papers 1106.5040, arXiv.org.
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    Cited by:

    1. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.

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