Asset Price and Wealth Dynamics Under Heterogeneous Expectations

In order to characterize asset price and wealth dynamics arising from theinteraction of heterogeneous agents with CRRA utility, a discrete-timestationary model in terms of return and wealth proportions (among differenttypes of agents) is established. When fundamentalists and chartists are themain heterogeneous agents in the model, it is found that in the presence ofheterogeneous 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 steadystate follows an optimal selectionprinciple-the return. and wealthproportions tend to the steady state which has relatively higher return. Moreimportantly, heterogeneity can generate instability which, under the stochasticprocesses of the dividend yield and extrapolation rates, results in switching ofthe return among different states, such as steady-state, periodic and aperiodiccycles from time to time. The model that is finally developed displays theessential characteristics of the standard asset price dynamics model assumedin continuous-time finance, in that the asset price is fluctuating around ageometrically growing trend. The model also displays the volatilityclustering that is an essential feature of empirically observed asset returns.