In recent years a large number of models of financial markets based on interacting heterogeneous agents have been developed. These models generally allow the size of the different groups of agents to vary according to the evolution of the financial market. Adaptive belief system proposed by Brock and Hommes (1997, 1998) are a typical example in recent studies of interacting heterogeneous models. This paper proposes a modified Brock-Hommes model with a stochastic learning process. We investigate the time series properties of this modified adaptive belief system, and show that the return series are characterized by fat tailed returns with clustered volatility that are considered to be the most important stylized facts in financial time series data. Furthermore we provide a mathematical explanation of the characteristics of the returns distribution analyzing the dynamics of our model. It is noteworthy is that the results of our analysis is very similar to those of Gaunersdorfer, Hommes (2000), and Gaunersdorfer, Hommes, and Wanger (2000) that have investigated the empirical and theoretical analyses of the dynamics in a adaptive belief system, in spite of introduction of a different system on choice of strategies. Second, we compare the modified adaptive belief system with the Lux-Marchesi model (Lux and Marchesi (1999)) as another example of interacting heterogeneous models that have been developed recently. We show that the two models share the common mathematical mechanisms that give cause to volatility clustering. References 1 Brock, W.A., and Hommes, C.H., (1997), Models of complexity in economics and finance, In: Hey, C., Schumacher, J.M., Hanzon, B., and Praagman, C.,eds., System Dynamics in Economic and Financial Model, Chapter 1, Wiely Publ., 3-41. 2 Brock, W.A., and Hommes, C.H., (1998), Heterogeneous beliefs and routesto chaos in a simple asset pricing model, Journal of Economic Dynamics and Control, 22, 1235-74. 3 Gaunersdorfer, A., and Hommes, C. H., (2000), A NonlinearStructural Model fro Volatility Clustering, CeNDEF working paper, University of Amsterdam. 4 Gaunersdorfer, A., and Hommes, C. H., and Wangener, F.O.J., (2000) Bifurcation routes to volatility clustering, CeNDEF working paper, University of Amsterdam. 5 Lux, T. and Marchesi, M., (1999), Scaling and criticality in a stochastic multi-agent model of a financial market, Nature 397, 498-500.
