A Dynamic Model for Systemic Risk in Networks Subject to Contagion

网络中的传染效应可能来自于网络中参与者的集体活动，也可能来自于直接相连的参与者之间的互动。这两个相互加强的相互联系渠道可能导致连锁网络故障和灾难，造成严重的社会后果。易受传染的网络系统的例子包括交通、电信和金融网络。 在某些环境中，网络级效应可以比通过相邻节点的扩散更快、更广地传播传染。 传染的蔓延可能会导致这些网络的功能崩溃。该项目将通过使用动态模型来识别这两个渠道的传染效应，以减轻传染的破坏性影响。该研究有望为决策者和风险管理专业人员提供新的决策工具，用于解决假设问题，为单个决策单元设计压力测试，监控网络中的关键元素，以及设置防火墙以防止或限制级联故障。互联网络中的传染动力学将被建模为高维动态互补问题，也称为Skorohod问题。解决Skorohod问题的算法将生成任何给定范围内的所有可能的故障时间，沿着网络状态的演化动态。这些结果将告知新的风险措施的失败和传染集中的集群的发展。另外的研究目标是：（1）对故障聚集和传染措施进行敏感性分析，建立一个鲁棒的优化模型来构建网络结构，并用数据对模型进行校准;（2）将随机冲击引入状态变量，研究故障和传染的状态和时间依赖动态;以及（3）研究资源控制方案以减轻传染，沿着效用最大化目标和公平约束。该项目将扩展随机网络的研究前沿，以产生新的方法来建模和分析网络中的系统性风险，以及理解故障传染动力学的新知识。

The contagion effect in a network may arise from the collective activities of the parties involved in the network as a whole, as well as from the interactions among parties who are directly connected to each other. These two mutually enhancing channels of interconnectedness can lead to cascading network failures and catastrophe with serious societal consequences. Examples of networked systems subject to contagion include traffic, telecommunication and financial networks. In some environments, the network-level effect can spread the contagion must faster and wider than the diffusion through neighboring nodes. Instances of contagion may cause functional collapse of such networks. This project will seek to mitigate the damaging effects of contagion via the use of a dynamic model to discern the effects of contagion from these two channels. This research is expected to lead to new decision tools that may be used by policy makers and risk management professionals to address what-if questions, to design stress tests for individual decision-making units, to monitor critical elements in a network, and to set up firewalls to prevent or limit cascading failures.Contagion dynamics in interconnected networks will be modeled as a high dimensional dynamic complementarity problem, also known as Skorohod problem. An algorithm that solves the Skorohod problem will generate all possible failure times over any given horizon, along with the evolution dynamics of the network state. These results will inform the development of new risk measures for clustering of failures and contagion concentration. Additional research objectives are: (1) conducting sensitivity analysis for the failure-clustering and contagion measures, formulating a robust optimization model to construct the network configuration and calibrating the model with data; (2) incorporating stochastic shocks to state variables to study the state- and time-dependent dynamics of failures and contagion; and (3) investigating resource control schemes to mitigate contagion, along with utility-maximizing objectives and fairness constraints. The project will extend the research frontier of stochastic networks to generate new approaches to modeling and analyzing systemic risk in networks, and new knowledge in understanding the contagion dynamics of failures.