Before revision:  The stock price is determined by the inflow or outflow of stock investments. The model is able to replicate the most prominent features of financial markets, namely booms and crashes. In the case of random fundamental prices the model is even able to reproduce fat tails in logarithmic stock price return data. We want to point out that we derive the model from microscopic agent dynamics. On the microscopic level each financial agent is faced with an optimization problem, where each agent seeks to find a Nash equilibrium solution. We use model predictive control to approximate the control problem.
After revision:  The stock price evolution is driven by the aggregated investment decision of all agents. In fact, we are faced with a differential game since all agents aim to invest optimal. Mathematically such a problem is ill posed and we introduce the concept of Nash equilibrium solutions to ensure the existence of a solution. Especially, we denote an agent who solves this Nash equilibrium exactly a rational agent. As next step we use model predictive control to approximate the control problem.