A Dynamic Model for Systemic Risk in Networks Subject to Contagion

Columbia University, New York NY

Investigators

Abstract

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.