We consider a model for systemic risk comprising of a system of diffusion processes, interacting through their empirical mean. Each process is subject to a confining double-well potential with some uncertainty in the coefficients, corresponding to fluctuations in height of the potential barrier seperating the two wells. This is equivalent to studying a single McKean-Vlasov SDE with explicit dependence on its moments and, novelly, independently varying additive and multiplicative noise. Such non-linear SDEs are known to possess two phases: stable (ordered) and unstable (disordered). When the potential is purely bistable, the phase changes from stable to unstable when noise intensity is increased past a critical threshold. With the recent advances, it will be shown that the behaviour here is far richer: indeed, depending on the interpretation of the stochastic integral, the system exhibits phase changes that cannot occur in any regime where there is no uncertainty in the potential. Strikingly, this allows for the phenomenon of noise induced stability; situations where more noise can reduce the risk of system failure.
Asymptotics of Systemic Risk in a Renewal Model with Multiple Business Lines and Heterogeneous Claims
School of Big Data and Statistics, Anhui University（安徽大学大数据与统计学院）；School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）理工学院）
Linear-quadratic optimal control for non-exchangeable mean-field SDEs and applications to systemic risk
Université Paris Cité（巴黎西岱大学）；Sorbonne University（索邦大学）；Institut für Mathematik, Technische Universität Berlin（柏林工业大学数学研究所）；Luiss Guido Carli University（鲁伊西斯·圭多·卡利大学）；Ecole Polytechnique（巴黎综合理工学院）
