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Abstract: Within a continuous-time framework, this paper proposes a stochastic heterogeneous agent model (HAM) of financial markets with time delays to unify various moving average rules used in discrete-time HAMs. The time delay represents a memory length of a moving average rule in discrete-time HAMs. Intuitive conditions for the stability of the fundamental price of the deterministic model in terms of agents’ behavior parameters and memory length are obtained. It is found that an increase in memory length not only can destabilize the market price, resulting in oscillatory market price characterized by a Hopf bifurcation, but also can stabilize an otherwise unstable market price, leading to stability switching as the memory length increases. Numerical simulations show that the stochastic model is able to characterize long deviations of the market price from its fundamental price and excess volatility and generate most of the stylized facts observed in financial markets. [ABSTRACT FROM AUTHOR]

Abstract: This paper develops a dynamic model of a financial market where heterogeneous agents invest among multiple risky assets and a risk-free asset, under a market maker scenario. Particular attention is paid to the case of two risky assets and two agent types, fundamentalists and trend chasers, whose beliefs on both first and second moments of the conditional distribution of returns are based on past observations. Conditions for the stability of the “fundamental” equilibrium are established and the effect of the correlation between the risky assets is examined. It turns out that investors’ anticipated correlation and dynamic portfolio diversification do not always have a stabilizing role, but rather may act as a source of complexity in the financial market. [Copyright &y& Elsevier]