Peer-to-Peer Risk-Sharing Schemes with Heterogeneity and Infinite-Mean Losses
Tim J. Boonen, Ka Long Chiu · North American Actuarial Journal · 2026
The increasing intensity of extreme catastrophic events in recent years highlights the critical need for insurance to protect against their potential disastrous impacts. However, such catastrophic losses are often regarded as uninsurable by insurers, and there is a lack of risk-management solutions for them. Contrary to basic intuition, the literature has shown that within a specific class of risk-sharing rules, diversifying infinite-mean Pareto losses is always harmful. Consequently, the optimal action is non-diversification, which effectively leads to a lack of protection against such catastrophic risks. In this article, by considering a broader class of risk-sharing rules, we construct novel risk-sharing mechanisms as alternatives to non-diversification for managing catastrophic Pareto risks. To establish a foundation, we first study linear risk-sharing rules in a peer-to-peer risk-sharing setting with heterogeneity. Within this class, a Pareto optimal risk-sharing rule is obtained: uniform risk sharing among agents with finite-mean Pareto losses and no risk sharing among agents with infinite-mean Pareto losses. Next, by introducing nonlinearity, we construct two novel risk-sharing rules for managing infinite-mean catastrophic Pareto risks. We then present theoretical results to justify the benefits of the proposed risk-sharing rules, supported by numerical illustrations.