A Mathematical Framework for Modeling Order Book Dynamics

We present a general framework for modeling the dynamics of limit order books, built on the combination of two modeling ingredients: the order flow, modeled as a general spatial point process, and market clearing, modeled via a deterministic ``mass transport"" operator acting on the distributions of buy and sell orders. At the mathematical level, this leads to a natural decomposition of the infinitesimal generator describing the evolution of the limit order book into two operators: the generator of the order flow and a clearing operator. This decomposition provides a flexible and modular framework for modeling and simulating order book dynamics and studying various scaling limits of discrete order book models. We show that our framework includes previous models as special cases and yields insights into the interplay between order flow and price dynamics.