Bewaard in:
| Hoofdauteurs: | , |
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| Formaat: | Preprint |
| Gepubliceerd in: |
2024
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| Onderwerpen: | |
| Online toegang: | https://arxiv.org/abs/2408.08511 |
| Tags: |
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Inhoudsopgave:
- 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.