On some extended mixed integer optimization models of the Eisenberg–Noe model in systemic risk management

Abstract

AbstractThe Eisenberg and Noe (EN) model has been widely adopted in the systemic risk management for financial networks. In this paper, we propose a unified EN (U‐EN) model, which incorporates both liquidation and bankruptcy costs. We show that the U‐EN model is polynomial‐time solvable and develop an efficient greedy algorithm to solve it. Then we consider identifying the optimal bailout strategy based on stress testing background and propose a binary EN model with bailout budget constraint (B‐EN‐B). The B‐EN‐B model is shown to be NP‐hard. We present analysis on the parameter selection and design some preprocessing procedures correspondingly. A sequential coefficient strengthening algorithm is designed to solve the B‐EN‐B model. Global convergence of the algorithm is established. Moreover, we show that the systemic risk level obtained from the B‐EN‐B model can be used as a precaution for the social planner. Experiments based on both simulated data and data from the Chinese listed banks' network are reported to demonstrate the efficiency of the proposed algorithms.