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

Çağın Ararat () and Nurtai Meimanjan ()
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Çağın Ararat: Department of Industrial Engineering, Bilkent University, 06800 Ankara, Turkey
Nurtai Meimanjan: Institute for Statistics and Mathematics, Vienna University of Economics and Business, 1020 Vienna, Austria

Operations Research, 2023, vol. 71, issue 6, 2130-2145

Abstract: 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 have been 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 an extension of the Rogers–Veraart network model where the operating cash flows are unrestricted in sign. We propose a mixed-integer programming problem that can be used to compute clearing vectors in this model. Because of the binary variables in this problem, the corresponding (set-valued) systemic risk measure fails to have convex values in general. We associate nonconvex vector optimization problems with the systemic risk measure and provide theoretical results related to the weighted-sum and Pascoletti–Serafini scalarizations of this problem. Finally, we test the proposed formulations on computational examples and perform sensitivity analyses with respect to some model-specific and structural parameters.

Keywords: Financial Engineering; systemic risk measure; set-valued risk measure; Eisenberg–Noe model; Rogers–Veraart model; mixed-integer programming; vector optimization (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:71:y:2023:i:6:p:2130-2145

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