Complex Dynamics in an Asset Pricing Model with Updating Wealth

Abstract

In recent years, several models have focused on the study of the asset price dynamics and wealth distribution when the economy is populated by boundedly rational heterogeneous agents with Constant Relative Risk Aversion (CRRA) preferences. Chiarella and He (2001) study an asset pricing model with heterogeneous agents and fixed population fractions. In order to obtain a more appealing framework, Chiarella and He (2002) allow agents to switch between different trading strategies. More recently, Chiarella et al. (2006) consider a market maker model of asset pricing and wealth dynamics with fixed proportions of agents. A large part of contributions to the development and analysis of financial models with heterogeneous agents and CRRA utility do not consider that agents can switch between different predictors. Moreover, the models which allow agents to switch between different trading strategies make the following simplified assumption: when agents switch from an old strategy to a new strategy, they agree to accept the average wealth level of agents using the new strategy. Motivated by such considerations, we develop a new model based upon a more realistic assumption. In fact, we assume that all agents belonging to the same group agree to share their wealth whenever an agent joins the group (or leaves it). The most important fact is that the wealth of the new group takes into account the wealth realized in the group of origin, whenever agents switch between different trading strategies. This leads the final system to a particular form, in which the average wealth of agents is defined by a continuous piecewise function and the phase space is divided into two regions. Nevertheless, our final dynamical system is three dimensional and we can find all the equilibria. We will prove that it admits two kinds of steady states, fundamental steady states (with the price being at the fundamental value) and non fundamental steady states. Several numerical simulations supplement the analysis.