Interacting Agent Feedback Finance Model

We consider a financial market model which consists of a financial asset and a large number of interacting agents classified into many types. Different types of agents are heterogeneous in their price expectations. Each agent can change its type based on the current empirical distribution of the types and the equilibrium price, and the equilibrium price follows a recursive price mechanism based on the previous price and the current empirical distribution of the types. The interaction among the agents, and the interaction between the agents and the equilibrium price, feedback, are modeled. We analyze the asymptotic behavior of the empirical distribution of the types and the equilibrium price when the number of agents goes to infinity. We give a case study of a simple example, and also investigate the fixed points of empirical distribution and equilibrium price of the example.