Browsing by Subject "Systemic risk measure"

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Open Access
Computation of systemic risk measures: a mixed-integer programming approach
(INFORMS Inst.for Operations Res.and the Management Sciences, 2023-09-22) Ararat, Çaǧın; Meimanjan, N.
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. Copyright: © 2023 INFORMS.
Open Access
Systemic risk measures based on value-at-risk
(2023-07) Al-Ali, Wissam
This thesis addresses the problem of computing systemic set-valued risk measures. The proposed method incorporates the clearing mechanism of the Eisenberg-Noe model, used as an aggregation function, with the value-at-risk, used as the underlying risk measure. The sample-average approximation (SAA) of the corresponding set-valued systemic risk measure can be calculated by solving a vector optimization problem. For this purpose, we propose a variation of the so-called grid algorithm in which grid points are evaluated by solving certain scalar mixed-integer programming problems, namely, the Pascoletti Serafini and norm-minimizing scalarizations. At the initialization step, we solve weighted sum scalarizations to establish a compact region for the algorithm to work on. We prove the convergence of the SAA optimal values of the scalarization problems to their respective true values. More-over, we prove the convergence of the approximated set-valued risk measure to the true set-valued risk measure in both the Wijsman and Hausdorff senses. In order to demonstrate the applicability of our findings, we construct a financial network based on the Bollob´as preferential attachment model. In addition, we model the economic disruptions using identically distributed random variables with a Pareto distribution. We conduct a comprehensive sensitivity analysis to investigate the effect of the number of scenarios, correlation coefficient, and Bollob´as network parameters on the systemic risk measure. The results highlight the minimal influence of the number of scenarios and correlation coefficient on the risk measure, demonstrating its stability and robustness, while shedding light on the profound significance of Bollob´as network parameters in determining the network dynamics and the overall level of systemic risk.