title: Anomalous impact in reaction-diffusion financial models.
abstract: We generalize the reaction-diffusion model A+B→0 in order to study the impact of an excess of A (or B) at the reaction front. We provide an exact solution of the model, which shows that the linear response breaks down: the average displacement of the reaction front grows as the square root of the imbalance. We argue that this model provides a highly simplified but generic framework to understand the square-root impact of large orders in financial markets.
authors.affiliation: Centre de Mathématiques Appliquées, CNRS, UMR7641, Ecole Polytechnique, 91128 Palaiseau, France.
authors.forename: I
authors.initials: I
authors.lastname: Mastromatteo
authors.affiliation: Capital Fund Management, 23-25 Rue de l'Université, 75007 Paris, France.
authors.forename: B
authors.initials: B
authors.lastname: Tóth
authors.affiliation: Capital Fund Management, 23-25 Rue de l'Université, 75007 Paris, France.
authors.forename: J-P
authors.initials: JP
authors.lastname: Bouchaud