Limit Theorems for Default Contagion and Systemic Risk

• 成果类型: Article
• 署名作者: Amini, Hamed; Cao, Zhongyuan; Sulemb, Agnes
• 署名单位: State University System of Florida; University of Florida; Universite PSL; Universite Paris-Dauphine
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.0283
• 发表日期: 2024
• 页码: 2652-2683
• 关键词: bootstrap percolation; Financial networks; MARKET; core

摘要

We consider a general tractable model for default contagion and systemic risk in a heterogeneous financial network subjected to an exogenous macroeconomic shock. We show that under certain regularity assumptions, the default cascade model can be transformed into a death process problem represented by a balls-and-bins model. We state various limit theorems regarding the final size of default cascades. Under appropriate assumptions on the degree and threshold distributions, we prove that the final sizes of default cascades have asymptotically Gaussian fluctuations. We next state limit theorems for different system-wide wealth aggregation functions, which enable us to provide systemic risk measures in relation to the structure and heterogeneity of the financial network. Lastly, we demonstrate how these results can be utilized by a social planner to optimally target interventions during a financial crisis given a budget constraint and under partial information of the financial network.