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Optimal posting price of limit orders: learning by trading |
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| Authors: | Sophie Laruelle Charles-Albert Lehalle Gilles Pagès |
| Institution: | 1. Laboratoire de Mathématiques Appliquées aux Systèmes, école Centrale Paris, Grande Voie des Vignes, 92290, Chatenay-Malabry, France 2. Crédit Agricole Cheuvreux, CALYON Group, 9 quai Paul Doumer, 92920, Paris La Défense, France 3. Laboratoire de Probabilités et Modèles Aléatoires, UMR?7599, UPMC, case 188, 4, pl. Jussieu, Paris Cedex 5, France |
| Abstract: | We model a trader interacting with a continuous market as an iterative algorithm that adjusts limit prices at a given rhythm and propose a procedure to minimize trading costs. 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 met (notably, using the co-monotony principle). We illustrate our results with numerical experiments on both simulated and market data. |
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