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arXiv · 2504.06287

Jointly Exchangeable Collective Risk Models: Interaction, Structure, and Limit Theorems

Daniel Gaigall·Stefan Weber
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Abstract

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.

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Daniel Gaigall, Stefan Weber. 2025-04-02. Jointly Exchangeable Collective Risk Models: Interaction, Structure, and Limit Theorems. https://arxiv.org/abs/2504.06287

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