  This paper characterizes the probability of a market failure defined as the
default of two or more globally systemically important banks (G-SIBs) in a
small interval of time. The default probabilities of the G-SIBs are correlated
through the possible existence of a market-wide stress event. The
characterization employs a multivariate Cox process across the G-SIBs, which
allows us to relate our work to the existing literature on intensity-based
models. Various theorems related to market failure probabilities are derived,
including the probability of a market failure due to two banks defaulting over
the next infinitesimal interval, the probability of a catastrophic market
failure, the impact of increasing the number of G-SIBs in an economy, and the
impact of changing the initial conditions of the economy's state variables. We
also show that if there are too many G-SIBs, a market failure is inevitable,
i.e., the probability of a market failure tends to 1.
