Before revision:  In fact the model can be regarded as  the result of the simplest approximation of the optimal control problem and thus considers financial agents of maximum boundedness. Mathematically, the model can be regarded as the moment model of the recently introduced mesoscopic kinetic portfolio model(Trimborn, Pareschi, Frank: Portfolio Optimization and Model Predictive Control: A Kinetic Approach, arXiv:1711.03291) .
After revision:  In fact the model can be regarded as the expected missed revenue of an agent and we assume quadratic transaction costs. More precisely the expected revenues are determined by a combination of a fundamentalist or chartist strategy. Then we derive the mean field limit of the microscopic model in order to obtain a macroscopic portfolio model. The novelty in comparison to existent macroeconomic models in literature is that our model is derived from microeconomic dynamics. The resulting portfolio model is a three dimensional ODE system which enables us to derive analytical results. Simulations reveal, that our model is able to replicate the most prominent features of financial markets, namely booms and crashes .