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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.

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File URL: http://arxiv.org/pdf/1112.2397
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1112.2397.

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Date of creation: Dec 2011
Date of revision: Sep 2012
Handle: RePEc:arx:papers:1112.2397

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Web page: http://arxiv.org/

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References

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  1. Foucault, Thierry & Kadan, Ohad & Kandel, Eugene, 2001. "Limit Order Book as a Market for Liquidity," CEPR Discussion Papers, C.E.P.R. Discussion Papers 2889, C.E.P.R. Discussion Papers.
  2. Guéant, Olivier & Lehalle, Charles-Albert & Tapia, Joaquin Fernandez, 2011. "Dealing with the Inventory Risk," Economics Papers from University Paris Dauphine 123456789/7390, Paris Dauphine University.
  3. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 8(3), pages 217-224.
  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, Taylor & Francis Journals, vol. 10(2), pages 143-157.
  6. Erhan Bayraktar & Michael Ludkovski, 2011. "Liquidation in Limit Order Books with Controlled Intensity," Papers 1105.0247, arXiv.org, revised Jan 2012.
  7. 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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Cited by:
  1. Olivier Gu\'eant & Charles-Albert Lehalle, 2012. "General Intensity Shapes in Optimal Liquidation," Papers 1204.0148, arXiv.org, revised Jun 2013.

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