Anomalous impact in reaction-diffusion 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 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.

5 pages, 2 figures

References in corpus (10)

• Price Variations in a Stock Market With Many Agents
• Market impact and trading profile of large trading orders in stock markets
• Anomalous price impact and the critical nature of liquidity in financial markets
• Modeling the Searching Behavior of Social Monkeys
• Agent-based models for latent liquidity and concave price impact
• The Reaction-Diffusion Front for $A+B\to \varnothing$ in One Dimension
• Refined Simulations of the Reaction Front for Diffusion-Limited Two-Species Annihilation in One Dimension
• How markets slowly digest changes in supply and demand
• Reaction-Diffusion-Branching Models of Stock Price Fluctuations
• Field Theoretic Approach to Long Range Reactions

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