A Heterogeneous Agent Model of Asset Price with Three Time Delays

Abstract

This paper considers a continuous-time heterogeneous agent model of a financial market with one risky asset, two types of agents (i.e., the fundamentalists and the chartists), and three time delays. The chartist's demand is determined through a nonlinear function of the difference between the current price and a weighted moving average of the delayed prices whereas the fundamentalist's demand is governed by the difference between the current price and the fundamental value. The asset price dynamics is described by a nonlinear delay differential equation. Two main results are analytically and numerically shown:(i) a single delay destabilizes the market price and generates cyclic oscillations around the equilibrium; (i) under multiple delays, stability loss and gain repeatedly occur as the length of the delay increases.