Heterogeneous Beliefs and Adaptive Behaviour in a Continuous-Time Asset Price Model

This paper extends the analysis of the seminal paper of Brock and Hommes (1998) on heterogeneous beliefs and routes to chaos in a simple asset price model in discrete-time to a model in continuous-time. The resulting model characterized mathematically by a system of stochastic delay differential equations provides a unified approach to deal with adaptive behaviour of heterogeneous agents and stability impact of lagged price information used by chartists to form their expectations. For the underlyingd eterministic model, we show not only that the result of Brock and Hommes on rational routes to market instability in discrete-time holds in continuous time but also a double edged effect of an increase in lagged price information used by the chartists on market stability. For the stochastic model, we demonstrate that the model is able to display various market phenomena such as bubbles and crashes and replicate stylized facts including volatility clustering, and long range dependence in volatility.