A Dynamic Model for Systemic Risk in Networks Subject to Contagion

网络中的传染效应可能源于整个网络中涉及的各方的集体活动，也可能来自彼此直接相连的各方之间的相互作用。这两个相互加强的互连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。在一些环境中，网络层面的效应可以传播，传播速度和范围必须比通过邻近节点的传播更快、更广。传染的情况可能会导致此类网络的功能崩溃。该项目将寻求通过使用动态模型来辨别这两个渠道的传染影响，以减轻传染的破坏性影响。这项研究有望产生新的决策工具，供政策制定者和风险管理专业人员使用，以解决假设问题，为单个决策单元设计压力测试，监控网络中的关键元素，并建立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问题的算法将在任何给定的水平上生成所有可能的故障时间，以及网络状态的演化动态。这些结果将为开发新的故障聚集和传染集中的风险措施提供信息。其他研究目标包括：(1)对故障聚集和传染措施进行灵敏度分析，建立稳健的优化模型来构建网络结构，并用数据校准模型；(2)将随机冲击引入状态变量，以研究故障和传染的状态和时间相关的动力学；(3)研究资源控制方案，以减少传染，以及效用最大化目标和公平性约束。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风险，并在理解故障的传染动力学方面产生新的知识。

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.