 Centralized systemic risk control in the interbank system: Weak formulation and Gamma-convergenceLijun Bo, Tongqing Li and Xiang Yu Stochastic Processes and their Applications, 2022, vol. 150, issue C, 622-654 Abstract: This paper studies a systemic risk control problem by the central bank, which dynamically plans monetary supply to stabilize the interbank system with borrowing and lending activities. Facing both heterogeneity among banks and the common noise, the central bank aims to find an optimal strategy to minimize the average distance between log-monetary reserves of all banks and the benchmark of some target steady levels. A weak formulation is adopted, and an optimal randomized control can be obtained in the system with finite banks by applying Ekeland’s variational principle. As the number of banks grows large, we prove the convergence of optimal strategies using the Gamma-convergence argument, which yields an optimal weak control in the mean field model. It is shown that this mean field optimal control is associated to the solution of a stochastic Fokker–Planck–Kolmogorov (FPK) equation, for which the uniqueness of the solution is established under some mild conditions. Keywords: Interbank system; Weak formulation; Mean field control; Stochastic FPK equation; Gamma-convergence (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:150:y:2022:i:c:p:622-654 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2022.05.005 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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