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

报告人：薄立军

报告地点：腾讯会议ID：887 963 883

报告时间：2021年11月12日星期五9:30-10:30

报告摘要：

This talk discusses a systemic risk control problem by the central bank, which dynamically plans monetary supply for 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 and some prescribed capital levels for all banks. 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 further prove the convergence of optimal strategies using the Gamma-convergence arguments, which yields an optimal weak control in the mean field model. It is shown that the limiting optimal control is linked to a solution of a stochastic Fokker-Planck-Kolmogorov (FPK) equation. The uniqueness of the solution to the stochastic FPK equation is also established under some mild conditions.

主讲人简介：

薄立军，西安电子科技大学教授、硕士和博士毕业于南开大学概率论与数理统计专业，研究方向为随机分析、随机控制与金融数学。 2012年入选教育部新世纪优秀人才支持计划。先后主持国家自然科学基金面上项目2项 (数理学部)、中科院前沿科学重点研究计划-青年拔尖科学家项目。目前已在国际公认的概率统计、金融数学、管理和运筹学权威期刊Ann. Appl. Probab., Math. Finan., SIAM J. Finan. Math., SIAM J. Control & Optim., Math. Opers. Res., Finan. & Stoch., J. Banking & Finan., Queueing Syst.上发表学术论文40余篇，出版教材两部。目前担任中国概率统计学会会刊《应用概率统计》和美国数学科学研究所(AIMS)旗舰期刊《J. Dynamics & Games》编委。