Abstract:
This paper analyses the dynamics of a model of a share market consisting of two groups of traders:
fundamentalists, who base their trading decisions on the expectation of a rerum to the fundamental
value of the asset, and chartists, who base their trading decisions on an analysis of past price trends.
The model is reduced to a two-dimensional map whose global dynamic behaviour is analysed in
detail. The dynamics are affected by parameters measuring the strength of fundamentalist demand
and the speed with which chartists adjust their estimate of the trend to past price changes. The
parameter space is characterized according to the local stability/instability of the equilibrium point
as well as the non-invertibility of the map. The method of critical curves of non-invertible maps is
used to understand and describe the range of global bifurcations that can occur. It is also shown how
the knowledge of deterministic dynamics uncovered here can aid in understanding the behaviour
of stochastic versions of the model.
