A Stochastic Model for Cascading Failures in Financial Networks

In this article, 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 for 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 the absence of information on the covariance.