Stability and bifurcation in a simple heterogeneous asset pricing model

Stability and bifurcation analysis of deterministic systems has been widely used in modeling financial markets. We develop a simple pricing model with two types of rational traders, fundamentalists and chartists, in order to study well price behavior in financial markets, we use student t distribution to replace traditional normal distribution to describe fundamental price process. We study the stability and bifurcation of the underling deterministic system and use numerical simulation to study the dynamic of the stochastic system, including autocorrelations structures and high kurtosis of the returns. It is found that the fundamental price becomes stable (unstable) when the activities from both types of traders are balanced (unbalanced).