Asset price and wealth dynamics in a financial market with heterogeneous agents

This paper considers a discrete-time model of a financial market with one risky asset and one risk-free asset, where the asset price and wealth dynamics is determined by the interaction of two groups of agents, fundamentalists and trend extrapolators. In each period each group allocates its wealth between the risky asset and the safe asset according to myopic expected utility maximization, but the two groups have heterogeneous beliefs about the risky return over the next period. We assume that investors have CRRA utility, so that their optimal demands for each asset depend on their wealth. A market maker is assumed to adjust the price at the end of each trading period, on the basis of the excess demand. The model results in a high dimensional nonlinear discrete-time dynamical system, with growing price and wealth processes, but it is reduced to a stationary system in terms of asset returns and wealth shares of the two groups. It is shown that the market dynamics is highly dependent on the parameters which characterize agents" behavior and that in some cases a “fundamental†steady state coexists with other steady states or different attractors. In such cases, the role played by the initial condition (in particular the initial wealth shares) is analyzed in detail by means of numerical investigation of the basins of attraction