Intervention on default contagion under partial information in a financial network.

We study the optimal interventions of a regulator (a central bank or government) on the illiquidity default contagion process in a large, heterogeneous, unsecured interbank lending market. The regulator has only partial information on the interbank connections and aims to minimize the fraction of final defaults with minimal interventions. We derive the analytical results of the asymptotic optimal intervention policy and the asymptotic magnitude of default contagion in terms of the network characteristics. We extend the results of Amini, Cont and Minca's work to incorporate interventions and adopt the dynamics of Amini, Minca and Sulem's model to build heterogeneous networks with degree sequences and initial equity levels drawn from arbitrary distributions. Our results generate insights that the optimal intervention policy is "monotonic" in terms of the intervention cost, the closeness to invulnerability and connectivity. The regulator should prioritize interventions on banks that are systematically important or close to invulnerability. Moreover, the regulator should keep intervening on a bank once having intervened on it. Our simulation results show a good agreement with the theoretical results.