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

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.