Optimization Modeling and Techniques for Systemic Risk Assessment and Control in Financial Networks
Abstract
Since the financial crisis of 2007–2008, the assessment and control of the systemic risk in financial networks has become one of the most important and active research areas in economics and finance. In this tutorial, we will give a basic introduction to various optimization models. These include linear optimization (LO) problems with uncertain data on both sides of the constraints, linear optimization with nonconvex quadratic constraints, mixed integer linear optimization, and stochastic optimization. Our discussion focuses on the following three topics in the risk analysis of financial networks: (i) vulnerability analysis of a financial network when only limited information of the network is available and the assets are subject to market shocks, (ii) identification of the least stable network structures for fixed assets and exploration of the cascading failures in them, and (iii) policies and strategies for risk mitigation.
Specifically, we will demonstrate how classical LO theory can be used to assess the contagion in the network when complete information about the network is available, and we introduce new optimization theory to deal with the scenario when only limited information of the financial network is exposed. We show how conventional optimization techniques, such as alternative convex search and successive linear approximation, can help identify the least stable network structure, and we discuss under what circumstances these conventional optimization techniques may fail and what new optimization techniques need to be developed. We will also discuss how to combine advanced analysis in continuous optimization and graph modeling to identify the network structure. Open questions and challenges from both an optimization and financial perspective will be discussed as well.
Video of this TutORial from the 2018 INFORMS Annual Meeting in Phoenix, Arizona, November 6, 2018, is available at https://youtu.be/qaTKJRRSTxI.
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