Abstract
This work's main purpose is to understand the price dynamics in a generic limit order market, and illustrate a dynamical trading mechanism that can be applied to explore its market microstructure. First and foremost, we capture the iterative nature of the limit order market, and quantitatively identify its capacities as a means to develop switching schemes for the appearances of different sorts of traders. After formally introducing a dynamical trading system to replace the complex limit order market, we then study trading processes in that trading system from both deterministic and stochastic perspectives, in the purpose of recognizing conditions of general instability and stochastic stability in the trading system. In the final part of this work, the dynamics of the spread and mid-price in a controlled trading system will be investigated, which fairly serves to verify the robustness of stochastic stability appearing in an uncontrolled trading system.