In this paper, we show that herding phenomena in financial markets can be interpreted using the theoretical tools of pinning control. This is accomplished by viewing herding as a diffusion of a certain opinion in a network of financial agents, whose trading strategies dynamically depend on that of their neighbors according to a nonlinear state-dependent law. The interaction among the agents is modeled through a directed weighted graph, and following the logic of pinning control, we model the generic exogenous information triggering herding behavior as a control signal fed by an external entity to a subset of agents that, by virtue of the received information, can play the correct trading action. The topological conditions of partial pinning control theory enable us to predict the number of agents reaching consensus, i.e., the diffusion of information through the network, and thus the magnitude of the herding phenomenon triggered by the informed/pinned nodes. By testing our model of opinion dynamics in an artificial agent-based financial market, we prove that it is capable of replicating herding phenomena of different and predictable intensities.
Nonlinear Dynamics – Springer Journals
Published: Feb 12, 2018
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