Jointly Exchangeable Collective Risk Models: Interaction, Structure, and Limit Theorems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911423112675328 |
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| author | Gaigall, Daniel Weber, Stefan |
| author_facet | Gaigall, Daniel Weber, Stefan |
| contents | We introduce a framework for systemic risk modeling in insurance portfolios using jointly exchangeable arrays, extending classical collective risk models to account for interactions. Joint exchangeability is a more general probabilistic symmetric than de Finetti's exchangeability, characterized by the Aldous-Hoover-Kallenberg representation. We establish central limit theorems that asymptotically capture total portfolio losses, providing a theoretical foundation for approximations in large portfolios and over long time horizons. These approximations are validated through simulation-based numerical experiments. Additionally, we analyze the impact of dependence on portfolio loss distributions, with a particular focus on tail behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06287 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Jointly Exchangeable Collective Risk Models: Interaction, Structure, and Limit Theorems Gaigall, Daniel Weber, Stefan Risk Management Probability Mathematical Finance 91G45, 60F05 We introduce a framework for systemic risk modeling in insurance portfolios using jointly exchangeable arrays, extending classical collective risk models to account for interactions. Joint exchangeability is a more general probabilistic symmetric than de Finetti's exchangeability, characterized by the Aldous-Hoover-Kallenberg representation. We establish central limit theorems that asymptotically capture total portfolio losses, providing a theoretical foundation for approximations in large portfolios and over long time horizons. These approximations are validated through simulation-based numerical experiments. Additionally, we analyze the impact of dependence on portfolio loss distributions, with a particular focus on tail behavior. |
| title | Jointly Exchangeable Collective Risk Models: Interaction, Structure, and Limit Theorems |
| topic | Risk Management Probability Mathematical Finance 91G45, 60F05 |
| url | https://arxiv.org/abs/2504.06287 |