  We present a general framework for modelling the dynamics of limit order
books, built on the combination of two modelling ingredients: the order flow,
modelled as a general spatial point process, and market clearing, modelled via
a deterministic mass transport operator acting on distributions of buy and sell
orders. At the mathematical level, this corresponds 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 the clearing operator.
Our model provides a flexible framework for modelling 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.

Mathematical Finance