Abstract:
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 selectionprinciple-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 that 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.
