We consider a general tractable model for default contagion and systemic risk in a
heterogeneous financial network subjected to an exogenous macroeconomic shock. We
show that under certain regularity assumptions, the default cascade model can be transformed
into a death process problem represented by a balls-and-bins model. We state various
limit theorems regarding the final size of default cascades. Under appropriate assumptions
on the degree and threshold distributions, we prove that the final sizes of default
cascades have asymptotically Gaussian fluctuations. We next state limit theorems for
different system-wide wealth aggregation functions, which enable us to provide systemic
risk measures in relation to the structure and heterogeneity of the financial network.
Lastly, we demonstrate how these results can be utilized by a social planner to optimally
target interventions during a financial crisis given a budget constraint and under
partial information of the financial network.
