Financial price fluctuations in a stock market model with many interacting agents

Summary. We consider a financial market model with a large number of interacting agents. Investors are heterogeneous in their expectations about the future evolution of an asset price process. Their current expectation is based on the previous states of their neighbors and on a random signal about the mood of the market. We analyze the asymptotics of both aggregate behavior and asset prices. We give sufficient conditions for the distribution of equilibrium prices to converge to a unique equilibrium, and provide a microeconomic foundation for the use of diffusion models in the analysis of financial price fluctuations.Received: 16 April 2003, Revised: 1 March 2004, JEL Classification Numbers: D40, D84, G10.I thank Peter Bank, Dirk Becherer, Hans Föllmer, Peter Leukert, José Scheinkman, Alexander Schied, Ching-Tang Wu, and seminar participants at various institutions for many suggestions and discussions. Thanks are due to two anonymous referees and the editor, C.D. Aliprantis, for valuable comments which helped to improve the presentation of the results. Financial support of Deutsche Forschungsgemeinschaft via SFB 373, Quantification and Simulation of Economic Processes, Humboldt-Universität zu Berlin, and DFG Research Center Mathematics for Key Technologies (FZT 86) is gratefully acknowledged.