In order to characterize asset price and wealth dynamics arising from the interaction of heterogeneous agents with CRRA utility, a discrete-time stationary model in terms of return and wealth proportions (among different types of agents) is established. When fundamentalists and chartists are the main heterogeneous agents in the model, it is found that in the presence of heterogeneous agents the stationary model can have multiple steady states. The steady state is unstable when the chartists extrapolate strongly and (locally) stable when they extrapolate weakly. The convergence to the steady state follows an optimal selection principle-the return and wealth proportions tend to the steady state which has relatively higher return. More importantly, heterogeneity can generate instability which, under the stochastic processes of the dividend yield and extrapolation rates, results in switching of the return among different states, such as steady-state, periodic and aperiodic cycles from time to time. The model has is finally developed displays the essential characteristics of the standard asset price dynamics model assumed in continuous-time finance, in that the asset price is fluctuating around a geometrically growing trend. The model also displays the volatility clustering that is an essential feature of empirically observed asset returns.
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