Conformal risk sharing: certified cost allocation with participation guarantees

Sharing the financial impact of rare adverse events across a group can soften extreme individual bur dens, but any participant made worse off by the ar rangement has reason to leave. A credible mechan ism must therefore provide each agent with a trust worthy cap on their future obligation and should be deployed only if the aggregate harm across participants is bounded. We formalise this as the Certified Allocation Problem: from finite data and without distributional assumptions, find a redis tribution rule, produce obligation caps for every participant, and verify that no participant is made materially worse off. We propose Conformal Risk Sharing, which solves this problem by pairing an interpretable sharing policy with split conformal calibration. The sharing intensity is tuned on train ing data, while held-out calibration data produces distribution-free per-agent guarantees (valid under exchangeability). Experiments on synthetic and real-world data, including precipitation and energy cooperative data, confirm that the framework can substantially reduce extreme obligations for high risk agents while controlling harm to others.