A non-linear model of trading mechanism on a financial market

We introduce a prototype model in an attempt to capture some aspects of market dynamics simulating a trading mechanism. The model description starts with a discrete-space, continuous-time Markov process describing arrival and movement of orders with different prices. We then perform a re-scaling procedure leading to a deterministic dynamical system controlled by non-linear ordinary differential equations (ODEs). This allows us to introduce approximations for the equilibrium distribution of the model represented by fixed points of deterministic dynamics.