Abstract:
We consider the issues of stability and systemic risk in large complex financial networks, including the study of default contagion, fire sales and risk processes on networks. We consider a general tractable model for default contagion and systemic risk in a heterogeneous financial network, subject to an exogenous macroeconomic shock. We show that, under some regularity assumptions, the default cascade model can be transferred to a death process problem represented by a balls-and-bins model. We state various limit theorems regarding the final size of the default cascade. Under suitable assumptions on the degree and threshold distributions, we prove that the final size of default cascade has asymptotically Gaussian fluctuations. We next state limit theorems for different system-wide wealth aggregation functions, which allow us to provide systemic risk measures in relation with the structure and heterogeneity of the financial network. We show how to quantify the systemic risk for a financial network under partial information facing an outside shock. Then we present a general tractable framework for understanding the joint impact of fire sales and default cascades on systemic risk in complex financial networks. We finally study risk processes on large financial systems, when agents, located on a large network, receive losses from their neighbors.
Biography:
Zhongyuan Cao is a Postdoctoral Instructor of Mathematics at NYU Shanghai. He holds a Ph.D. in Applied Mathematics from Université Paris-Dauphine. He obtained a Master's Degree in Mathematics from Sorbonne Université. He conducts research in the intersection of systemic risk, stochastic control, weakly interacting particle systems and mean field game theory. He has broad interests in financial mathematics, probability theory and machine (deep) learning.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.