Optimal posting distance of limit orders: 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

This paper presents a stochastic recursive procedure under constraints to find the optimal distance at which an agent must post his order to minimize his execution cost. We prove the $a.s.$ convergence of the algorithm under assumptions on the cost function and give some practical criteria on model parameters to ensure that the conditions to use the algorithm are fulfilled (using notably principle of opposite monotony). We illustrate our results with numerical experiments on simulated data but also by using a financial market dataset.

Mots clés: Stochastic approximation; order book; limit order; market impact; statistical learning; high-frequency optimal liquidation; compound Poisson process; co-monotony principle

Domaines: Probabilités [math.PR]

Sophie Laruelle, Charles-Albert Lehalle, Gilles Pagès. Optimal posting distance of limit orders: a stochastic algorithm approach. 2011. ⟨hal-00650314v1⟩