AI 中文总结
该研究在非对称纳什议价框架下，结合价格公平与联盟稳定性条件，推导P2P保险最优合约的存在性与一阶表征，揭示价格公平及池规模对风险分配与福利的影响。
AI 中文摘要
我们在非对称纳什议价框架下研究风险厌恶型点对点（P2P）再保险机构与多个风险厌恶型对等方之间的P2P保险合约，其中所有主体都力求相对于其分歧点提高期望效用。与期望保费原理一致，我们施加价格公平条件，要求每个对等方的期望贡献基于对该对等方期望损失应用的共同加载项。为证明该议价公式相对于标准固定权重加权和优化问题的合理性，我们提供了公理化表征，表明纳什议价解满足适用于小型池中自愿P2P保险合约的性质。我们证明了最优合约的存在性与唯一性，并推导了全额、部分及零再保险 regimes 的一阶表征。为解决子群形成问题，我们开发了计算上可处理的充分条件，这些条件可排除可行的联盟偏离，无论是否存在价格公平。我们的数值研究考察了价格公平和池规模对最优合约及主体福利的影响：价格公平减少了对等方之间风险分配和确定性等价加载项的分散；关于池规模，福利并非单调增加，这表明风险池扩张不仅取决于多样化，还取决于议价能力的演变。
英文摘要
We study peer-to-peer (P2P) insurance contracting between a risk-averse P2P reinsurer and multiple risk-averse peers in an asymmetric Nash-bargaining framework, where all agents seek to improve expected utility relative to their disagreement points. Consistent with the expected value premium principle, we impose a price-fairness condition requiring each peer's expected contribution to be based on a common loading applied to the peer's expected loss. To justify the bargaining formulation relative to a standard fixed-weight weighted-sum optimization problem, we provide an axiomatic characterization showing that the Nash bargaining solution satisfies properties well suited to voluntary P2P insurance contracting in small pools. We establish the existence and uniqueness of the optimal contract and derive first-order characterizations for the full-, partial-, and zero-reinsurance regimes. To address subgroup formation, we develop computationally tractable sufficient conditions that rule out viable coalitional deviations, both with and without price fairness. Our numerical study investigates the impact of price fairness and pool size on the optimal contract and agents' welfare. Price fairness reduces dispersion in risk allocations and certainty-equivalent loadings among peers. Regarding pool size, welfare need not increase monotonically, highlighting that risk-pool expansion depends not only on diversification but also on the evolution of bargaining power.
