By John R. Birge, Jiming Peng, and Aein Khabazian.
Since the crisis in 2007-2008, the assessment and control of systemic risk in financial networks has become one of the most important and active research areas in economics and finance. In this tutorial, we give a basic introduction to various optimization models including linear optimization problems (LO) with uncertain data, linear optimization with non-convex quadratic constraints (QCLO), mixed integer linear optimization (MILO), and stochastic optimization that arise from the following three topics in the risk analysis of financial networks: (i) vulnerability analysis; (ii) identification of the least stable network structure; (iii) risk mitigation.