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

Sophie Laruelle (), Charles-Albert Lehalle and Gilles Pagès ()
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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
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

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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.

Keywords: Asset allocation; Stochastic Lagrangian algorithm; reinforcement principle; monotone dynamic system (search for similar items in EconPapers)
Date: 2011
Note: View the original document on HAL open archive server: https://hal.science/hal-00422427v3
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Published in SIAM Journal on Financial Mathematics, 2011, 2, pp.1042-1076

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Working Paper: Optimal split of orders across liquidity pools: a stochastic algorithm approach (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00422427

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