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. 
N. Vvedenskaya, Y. Suhov, V. Belitsky
q-fin.TR math.PR