A Stochastic Model for Cascading Failures in Financial Networks

Abstract

We study cascading failures in time-varying and uncertain financial networks. First we develop a stochastic dynamic model for the mean and covariance matrix of the market value of each company in the network. Second, we provide a steady-state analysis, we characterize equilibrium points and we provide conditions on the asymptotic stability of such points. For the covariance matrix the dynamics have the form of a Lyapunov equation and simulating such dynamics can be viewed as a numerical method to compute the steady-state solution. As a general insight, the dynamics reveal the probability of failure of each company during the transient and at steady-state. Finally, we perform a robust analysis to obtain bounding sets for the mean market value in absence of information on the covariance.