Centralized systemic risk control in the interbank system: Weak formulation and Gamma-convergence

This paper studies a systemic risk control problem by the central bank, which dynamically plans monetary supply to stabilize interbank system with borrowing and lending activities. Facing both heterogeneity among banks common noise, bank aims find an optimal strategy minimize average distance between log-monetary reserves of all benchmark some target steady levels. A weak formulation is adopted, randomized can be obtained in finite applying Ekeland’s variational principle. As number grows large, we prove convergence strategies using Gamma-convergence argument, yields mean field model. It shown that this associated solution stochastic Fokker–Planck–Kolmogorov (FPK) equation, for uniqueness established under mild conditions.