Jointly Exchangeable Collective Risk Models: Interaction, Structure, and Limit Theorems
Risk Management
2026-02-06 v2 Probability
Mathematical Finance
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.
Keywords
Cite
@article{arxiv.2504.06287,
title = {Jointly Exchangeable Collective Risk Models: Interaction, Structure, and Limit Theorems},
author = {Daniel Gaigall and Stefan Weber},
journal= {arXiv preprint arXiv:2504.06287},
year = {2026}
}