  In this paper, we propose a dynamical model to capture cascading failures
among interconnected organizations in the global financial system. Failures can
take the form of bankruptcies, defaults, and other insolvencies. The network
that underpins the financial interdependencies between different organizations
constitutes the backbone of the financial system. A failure in one or more of
these organizations can lead the propagation of the financial collapse onto
other organizations in a domino effect. Paramount importance is therefore given
to the mitigation of these failures. Motivated by the relevance of this problem
and recent prominent events connected to it, we develop a framework that allows
us to investigate under what conditions organizations remain healthy or are
involved in the propagation of the failures in the network. The contribution of
this paper is the following: i) we develop a dynamical model that describes the
equity values of financial organizations and their evolution over time given an
initial condition; ii) we characterize the equilibria for this model by proving
the existence and uniqueness of these equilibria, and by providing an explicit
expression for them; and iii) we provide a computational method via sign-space
iteration to analyze the propagation of failures and the attractive equilibrium
point.
