Heterogeneous beliefs and adaptive behaviour in a continuous-time asset price model

Xue-Zhong He, Kai Li

Research output: Contribution to journalArticlepeer-review

37 Citations (Scopus)


This paper extends the analysis of the seminal work of Brock and Hommes (1997, 1998) on heterogeneous beliefs and rational routes to randomness in discrete-time models to a continuous-time model of asset pricing. The resulting model characterised mathematically by a system of stochastic delay differential equations provides a unified approach to deal with adaptive behaviour of heterogeneous agents and market stability impact of lagged price used by chartists to form their expectations. For the underlying deterministic 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 used by the chartists on market stability. For the stochastic model, we demonstrate that the interaction and boundedly rational behaviour of heterogeneous agents can generate various market phenomena such as bubbles and crashes and replicate stylised facts including volatility clustering, and long range dependence in volatility.
Original languageEnglish
Pages (from-to)973-987
Number of pages15
JournalJournal of Economic Dynamics and Control
Issue number7
Publication statusPublished - Jul 2012
Externally publishedYes


  • heterogeneous beliefs
  • bounded rationality
  • adaptiveness
  • fundamentalists
  • chartists
  • stability
  • stochastic delay differential equations


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