Computation of Systemic Risk Measures: A Mixed-Integer Programming Approach

Abstract

Mixed-Integer Programming Formulations for Systemic Risk Measures Measurement and allocation of systemic risk have become important tasks in interconnected financial networks. In “Computation of Systemic Risk Measures: A Mixed-Integer Programming Approach,” Ararat and Meimanjan consider a clearing model that considers external assets and business costs of a bank simultaneously by extending the Rogers–Veraart network model with default costs. They prove that clearing payment vectors can be calculated by solving mixed-integer programming problems in which the existence of business costs and default costs are represented by binary variables. The systemic risk measure corresponding to this model yields nonconvex sets of capital allocation vectors. The authors compute these nonconvex sets by solving a multiobjective optimization problem whose scalarizations are two-stage mixed-integer programming problems with an expectation constraint. The computational procedure is versatile enough to accommodate other applications of systemic risk where the risk factors are aggregated by solving a general mixed-integer programming problem.