Optimization Based Methods for Systemic Risk Management

Columbia University, New York NY

Investigators

Abstract

The project will develop a general framework for defining risk measures for systems consisting of a set of interacting agents with uncertain joint outcomes. This framework will define convex programming-based axioms that characterize a very general class of systemic measures. This class of risk measures includes all the ad hoc risk measures that have been recently proposed in the literature. The optimization-based approach leads to a primal-dual representation for the systemic risk that allows attribution of the overall risk to individual agents in a fair manner, as well as the development of decentralized algorithms for systemic risk sensitive social welfare maximization. The project will seek to extend this representation to include a larger class of risk functions. New structural models will aid the study of the role of contagion in complex systems. A statistical methodology will be developed for identifying systemically important factors and the exposure of the system to these factors. These systemic factors would lead to methods for robust and efficient estimation of systemic risk. Systemic risk measure based algorithms for the design and control of the network structure underlying complex systems will also be explored. Recent events across many disparate settings (e.g., the Deepwater Horizon oil spill in 2010, the financial crisis in 2008, the Northeastern blackout in 2003) have all highlighted the critical importance of risk management in general, and systemic risk management in particular. Progress on tools for systemic risk management will help prevent, or at least better manage, future systemic failures in financial, public health, environmental, national security, and governmental domains. The proposed research is synergistic with ongoing relationships and collaborations the PIs maintain with industry and policy-making groups concerned with systemic risk in electricity grids and in capital markets. In addition, the project will provide funding for research and educational opportunities for students.