Systemic values-at-risk and their sample-average approximations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913469345824768 |
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| author | AlAli, Wissam Ararat, Çağın |
| author_facet | AlAli, Wissam Ararat, Çağın |
| contents | This paper investigates the convergence properties of sample-average approximations (SAA) for set-valued systemic risk measures. We assume that the systemic risk measure is defined using a general aggregation function with some continuity properties and value-at-risk applied as a monetary risk measure. We focus on the theoretical convergence of its SAA under Wijsman and Hausdorff topologies for closed sets. After building the general theory, we provide an in-depth study of an important special case where the aggregation function is defined based on the Eisenberg-Noe network model. In this case, we provide mixed-integer programming formulations for calculating the SAA sets via their weighted-sum and norm-minimizing scalarizations. To demonstrate the applicability of our findings, we conduct a comprehensive sensitivity analysis by generating a financial network based on the preferential attachment model and modeling the economic disruptions via a Pareto distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08511 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Systemic values-at-risk and their sample-average approximations AlAli, Wissam Ararat, Çağın Risk Management Optimization and Control Probability 26E25, 90C29, 91G45, 91G70 This paper investigates the convergence properties of sample-average approximations (SAA) for set-valued systemic risk measures. We assume that the systemic risk measure is defined using a general aggregation function with some continuity properties and value-at-risk applied as a monetary risk measure. We focus on the theoretical convergence of its SAA under Wijsman and Hausdorff topologies for closed sets. After building the general theory, we provide an in-depth study of an important special case where the aggregation function is defined based on the Eisenberg-Noe network model. In this case, we provide mixed-integer programming formulations for calculating the SAA sets via their weighted-sum and norm-minimizing scalarizations. To demonstrate the applicability of our findings, we conduct a comprehensive sensitivity analysis by generating a financial network based on the preferential attachment model and modeling the economic disruptions via a Pareto distribution. |
| title | Systemic values-at-risk and their sample-average approximations |
| topic | Risk Management Optimization and Control Probability 26E25, 90C29, 91G45, 91G70 |
| url | https://arxiv.org/abs/2408.08511 |