A Particle Model for the Herding Phenomena Induced by Dynamic Market Signals

In this paper, we study herding phenomena of agents in financial markets arising from the combined effect of (1) non-coordinated collective interactions between agents and (2) concurrent reactions of agents to dynamic market signals. By interpreting the expected price of an asset and the favorability on the asset as the position and the velocity in phase space, respectively, we construct an agent-based particle model for explaining herding behavior in finance. We then define two types of herding functionals to this model, and show that they satisfy a Gronwall type estimate and a LaSalle type invariance property, respectively. As a result, we show the herding behavior of the agents. Various numerical tests are presented to numerically verify theoretical results.