A Dynamic Contagion Risk Model with Recovery Features

• 成果类型: Article
• 署名作者: Amini, Hamed; Minca, Andreea; Sulem, Agnes
• 署名单位: University System of Georgia; Georgia State University; Cornell University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1174
• 发表日期: 2022
• 页码: 1412-1442
• 关键词: bootstrap percolation; Financial networks; Systemic risk; STABILITY

摘要

We introduce threshold growth in the classical threshold contagion model, or equivalently a network of Cramer-Lundberg processes in which nodes have downward jumps when there is a failure of a neighboring node. Choosing the configuration model as underlying graph, we prove fluid limits for the baseline model, as well as extensions to the directed case, state-dependent interarrival times and the case of growth driven by upward jumps. We obtain explicit ruin probabilities for the nodes according to their characteristics: initial threshold and in- (and out-) degree. We then allow nodes to choose their connectivity by trading off link benefits and contagion risk. We define a rational equilibrium concept in which nodes choose their connectivity according to an expected failure probability of any given link and then impose condition that the expected failure probability coincides with the actual failure probability under the optimal connectivity. We show existence of an asymptotic equilibrium and convergence of the sequence of equilibria on the finite networks. In particular, our results show that systems with higher overall growth may have higher failure probability in equilibrium.