Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic risk measures are proposed in the literature that are used to determine capital requirements for the members subject to joint risk considerations. We address the problem of computing systemic risk measures for systems with sophisticated clearing mechanisms. In particular, we consider the Eisenberg-Noe network model and the Rogers-Veraart network model, where the former one is extended to the case where operating cash flows in the system are unrestricted in sign. We propose novel mixed-integer linear programming problems that can be used to compute clearing vectors for these models. Due to the binary variables in these problems, the corresponding (set-valued) systemic risk measures fail to have convex values in general. We associate nonconvex vector optimization problems to these systemic risk measures and solve them by a recent nonconvex variant of Benson's algorithm which requires solving two types of scalar optimization problems. We provide a detailed analysis of the theoretical features of these problems for the extended Eisenberg-Noe and Rogers-Veraart models. We test the proposed formulations on computational examples and perform sensitivity analyses with respect to some model-specific and structural parameters.
Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic risk measures are proposed in the literature that are used to determine capital requirements for the members subject to joint risk considerations. We address the problem of computing systemic risk measures for systems with sophisticated clearing mechanisms. In particular, we consider the Eisenberg-Noe network model and the Rogers-Veraart network model, where the former one is extended to the case where operating cash flows in the system are unrestricted in sign. We propose novel mixed-integer linear programming problems that can be used to compute clearing vectors for these models. Due to the binary variables in these problems, the corresponding (set-valued) systemic risk measures fail to have convex values in general. We associate nonconvex vector optimization problems to these systemic risk measures and provide theoretical results related to the weighted-sum and minimum step-length scalarizations of these problems under the extended Eisenberg-Noe and Rogers-Veraart models. We test the proposed formulations on computational examples and perform sensitivity analyses with respect to some model-specific and structural parameters.
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solve them by a recent nonconvex variant of Benson's algorithm which requires solving two types of scalar optimization problems. We provide a detailed analysis of the theoretical features
provide theoretical results related to the weighted-sum and minimum step-length scalarizations
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