Dynamical analysis of a financial market with fundamentalists, chartists, and imitators

The aim of the paper is to understand the price dynamics generated by the interaction of traders relying on heterogeneous expectations in an asset pricing model. In the present work we propose a financial market populated by three types of agents – fundamentalists, chartists and imitators. The latter submit buying/selling orders according to different trading rules using a 2D Piecewise Linear (PWL) discontinuous map. Our contribution to the existing financial literature is twofold. First, we perform an analytical study of the model involving a 2D PWL discontinuous map, where mainly numerical results are provided by researchers, besides few exceptions. In particular, we investigate the bifurcations showed by the model and the large variety of dynamical behavior produced. Finally, we provide numerical simulations in order to highlight the interaction between traders with heterogeneous expectations that can lead to intricate bull and bear price dynamics.