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

Author

Listed:
  • Sophie Laruelle

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Charles-Albert Lehalle

    (Head of Quantitative Research - CALYON group)

  • Gilles Pagès

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Sophie Laruelle & Charles-Albert Lehalle & Gilles Pagès, 2011. "Optimal split of orders across liquidity pools: a stochastic algorithm approach," Post-Print hal-00422427, HAL.
    • Handle: RePEc:hal:journl:hal-00422427
    Note: View the original document on HAL open archive server: https://hal.science/hal-00422427v3
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    References listed on IDEAS

    as
    1. Thierry Foucault & Albert J. Menkveld, 2008. "Competition for Order Flow and Smart Order Routing Systems," Journal of Finance, American Finance Association, vol. 63(1), pages 119-158, February.
    2. Thierry Foucault & Albert J. Menkveld, 2006. "Competition for Order Flow Smart Order Routing Systems," Post-Print halshs-00125689, HAL.
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    Cited by:

    1. Florian Klock & Alexander Schied & Yuemeng Sun, 2012. "Price manipulation in a market impact model with dark pool," Papers 1205.4008, arXiv.org, revised May 2014.

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