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Optimal split of orders across liquidity pools: a stochastic algorithm approach

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  • Sophie Laruelle

    (PMA)

  • Charles-Albert Lehalle

    (PMA)

  • Gilles Pag\`es

    (PMA)

Abstract

Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize their execution. To solve this problem we devised two stochastic recursive learning procedures which adjust the proportions of the order to be sent to the different venues, one based on an optimization principle, the other on some reinforcement ideas. Both procedures are investigated from a theoretical point of view: we prove a.s. convergence of the optimization algorithm under some light ergodic (or "averaging") assumption on the input data process. No Markov property is needed. When the inputs are i.i.d. we show that the convergence rate is ruled by a Central Limit Theorem. Finally, the mutual performances of both algorithms are compared on simulated and real data with respect to an "oracle" strategy devised by an "insider" who knows a priori the executed quantities by every venues.

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File URL: http://arxiv.org/pdf/0910.1166
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0910.1166.

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Date of creation: Oct 2009
Date of revision: May 2010
Handle: RePEc:arx:papers:0910.1166

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Web page: http://arxiv.org/

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  1. Foucault, Thierry & Menkveld, Albert, 2006. "Competition for order flow and smart order routing systems," Les Cahiers de Recherche 831, HEC Paris.
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Cited by:
  1. 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.
  2. Robert Azencott & Arjun Beri & Yutheeka Gadhyan & Nicolas Joseph & Charles-Albert Lehalle & Matthew Rowley, 2013. "Realtime market microstructure analysis: online Transaction Cost Analysis," Papers 1302.6363, arXiv.org, revised Mar 2013.
  3. Bruno Bouchard & Ngoc-Minh Dang, 2013. "Generalized stochastic target problems for pricing and partial hedging under loss constraints—application in optimal book liquidation," Finance and Stochastics, Springer, Springer, vol. 17(1), pages 31-72, January.
  4. Olivier Gu\'eant & Charles-Albert Lehalle, 2012. "General Intensity Shapes in Optimal Liquidation," Papers 1204.0148, arXiv.org, revised Jun 2013.
  5. Mauricio Labadie & Charles-Albert Lehalle, 2012. "Optimal starting times, stopping times and risk measures for algorithmic trading: Target Close and Implementation Shortfall," Papers 1205.3482, arXiv.org, revised Dec 2013.
  6. Rama Cont & Arseniy Kukanov, 2012. "Optimal order placement in limit order markets," Papers 1210.1625, arXiv.org, revised Jul 2013.
  7. Florian Kl\"ock & Alexander Schied & Yuemeng Sun, 2012. "Price manipulation in a market impact model with dark pool," Papers 1205.4008, arXiv.org, revised May 2014.
  8. Rama Cont & Arseniy Kukanov, 2012. "Optimal order placement in limit order markets," Working Papers hal-00737491, HAL.
  9. Aim\'e Lachapelle & Jean-Michel Lasry & Charles-Albert Lehalle & Pierre-Louis Lions, 2013. "Efficiency of the Price Formation Process in Presence of High Frequency Participants: a Mean Field Game analysis," Papers 1305.6323, arXiv.org, revised Mar 2014.
  10. Charles-Albert Lehalle, 2013. "Market Microstructure Knowledge Needed for Controlling an Intra-Day Trading Process," Papers 1302.4592, arXiv.org.
  11. Guéant, Olivier & Lehalle, Charles-Albert & Tapia, Joaquin Fernandez, 2011. "Optimal Portfolio Liquidation with Limit Orders," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/7391, Paris Dauphine University.
  12. Guéant, Olivier & Lehalle, Charles-Albert & Tapia, Joaquin Fernandez, 2011. "Dealing with the Inventory Risk," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/7390, Paris Dauphine University.
  13. Mauricio Labadie & Charles-Albert Lehalle, 2012. "Optimal starting times, stopping times and risk measures for algorithmic trading," Working Papers hal-00705056, HAL.

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