We propose a peer-to-peer (P2P) insurance scheme comprising a risk-sharing pool and a reinsurer. A plan manager determines how risks are allocated among members and ceded to the reinsurer, while the reinsurer sets the reinsurance loading. Our work focuses on the strategic interaction between the plan manager and the reinsurer, and this focus leads to two game-theoretic contract designs: a Pareto design and a Bowley design, for which we derive closed-form optimal contracts. In the Pareto design, cooperation between the reinsurer and the plan manager leads to multiple Pareto-optimal contracts, which are further refined by introducing the notion of coalitional stability. In contrast, the Bowley design yields a unique optimal contract through a leader-follower framework, and we provide a rigorous verification of the individual rationality constraints via pointwise comparisons of payoff vectors. Comparing the two designs, we prove that the Bowley-optimal contract is never Pareto optimal and typically yields lower total welfare. In our numerical examples, the presence of reinsurance improves welfare, especially with Pareto designs and a less risk-averse reinsurer. We further analyze the impact of the single-loading restriction, which disproportionately favors members with riskier losses.

翻译：我们提出一种包含风险共担池与再保险商的点对点（P2P）保险方案。计划管理者决定风险如何在成员间分配以及向再保险商分出，而再保险商则设定再保险附加费率。本文聚焦于计划管理者与再保险商之间的策略互动，由此引出两种博弈论契约设计：帕累托设计与鲍利设计，并推导出两者的闭式最优契约。在帕累托设计中，再保险商与计划管理者的合作产生多个帕累托最优契约，通过引入联盟稳定性概念可进一步优化选择。相比之下，鲍利设计通过领导者-追随者框架产生唯一最优契约，并借助收益向量的逐点比较对个体理性约束进行了严格验证。通过比较两种设计，我们证明鲍利最优契约绝非帕累托最优，且通常导致更低的总福利。数值算例表明，再保险的引入能提升福利水平，尤其在采用帕累托设计且再保险商风险厌恶程度较低时效果更显著。我们进一步分析了单一附加费率限制的影响，发现该限制会对损失风险更高的成员产生不成比例的有利影响。