Optimal split of orders across liquidity pools: a stochastic algorithm approach
AbstractEvolutions 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 0910.1166.
Date of creation: Oct 2009
Date of revision: May 2010
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Web page: http://arxiv.org/
Other versions of this item:
- Sophie Laruelle & Charles-Albert Lehalle & Gilles Pagès, 2009. "Optimal split of orders across liquidity pools: a stochastic algorithm approach," Working Papers hal-00422427, HAL.
- NEP-ALL-2009-10-10 (All new papers)
- NEP-CMP-2009-10-10 (Computational Economics)
- NEP-MST-2009-10-10 (Market Microstructure)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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