Anomalous impact in reaction-diffusion models

TL;DR

This paper presents an exact solution to a generalized reaction-diffusion model, revealing that an imbalance causes the reaction front to grow with the square root of the excess, offering insights into market impact phenomena.

Contribution

It introduces a generalized reaction-diffusion model with an exact solution, demonstrating nonlinear response and providing a simplified framework for understanding large order impacts in markets.

Findings

Reaction front displacement grows as the square root of imbalance.

Linear response breaks down under excess conditions.

Model offers a generic framework for market impact analysis.

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 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.