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

Sophie Laruelle (1) , Charles-Albert Lehalle (2) , Gilles Pagès (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 Head of Quantitative Research

Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because liquidity issues the trading firms split large orders across 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 reinforcement ideas. We investigate both procedures from a theoretical point of view. In particular, we prove convergence results for the optimization algorithm when the innovations are supposed to be Markov stationary and ergodic (and speed with some mixing properties or when they are i.i.d.). Finally, we compare the behaviours of both algorithms on several simulations results (with simulated data and real data). We evaluate their performances with respect to an "oracle" strategy of an "insider" who could know \textit{a priori} the executed quantities by every venues.

Mots clés: Asset allocation; Stochastic Lagrangian algorithm; reinforcement principle; monotone dynamic system

Domaines: Probabilités [math.PR]

Sophie Laruelle, Charles-Albert Lehalle, Gilles Pagès. Optimal split of orders across liquidity pools: a stochastic algorithm approach. 2009. ⟨hal-00422427v1⟩