The effect of heterogeneity on flocking behavior and systemic risk. (arXiv:1607.08287v1 [q-fin.RM])

The goal of this paper is to study organized flocking behavior and systemic risk in heterogeneous mean-field interacting diffusions. We illustrate in a number of case studies the effect of heterogeneity in the behavior of systemic risk in the system. We also investigate the effect of heterogeneity on the "flocking behavior" of different agents, i.e., when agents with different dynamics end up behaving the same way in path space and follow closely the mean behavior of the system. Using Laplace asymptotics, we derive an asymptotic formula for the tail of the loss distribution as the number of agents grows to infinity. This characterizes the tail of the loss distribution and the effect of the heterogeneity of the network on the tail loss probability.