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