标题： 基于补偿的风险共担 显示英文标题

标题： Compensation-based risk-sharing

摘要： 本文研究了在一种满足完全分配的风险共享规则下，使用终值意外基金进行赔付（补偿）的数学问题。除了参与者外，管理员通过收集事前贡献来建立基金，并在事后向成员分配赔付。考虑了两种类型的管理员。一个“主动”管理员既投资于基金，在没有参与者获得赔付时也获得基金的赔付。一个“被动”管理员仅执行行政任务，既不投资也不从基金中获得赔付。我们分析了基于补偿的风险共享方案的精算公平性，并提供了实现公平的一般条件。这些结果扩展了Denuit和Robert（2025）以及Dhaene和Milevsky（2024）的早期工作，他们专注于基于伯努利分布的赔付，允许一般非负损失分布。 显示英文摘要

摘要： This paper studies the mathematical problem of allocating payouts (compensations) in an endowment contingency fund using a risk-sharing rule that satisfies full allocation. Besides the participants, an administrator manages the fund by collecting ex-ante contributions to establish the fund and distributing ex-post payouts to members. Two types of administrators are considered. An 'active' administrator both invests in the fund and receives the payout of the fund when no participant receives a payout. A 'passive' administrator performs only administrative tasks and neither invests in nor receives a payout from the fund. We analyze the actuarial fairness of both compensation-based risk-sharing schemes and provide general conditions under which fairness is achieved. The results extend earlier work by Denuit and Robert (2025) and Dhaene and Milevsky (2024), who focused on payouts based on Bernoulli distributions, by allowing for general non-negative loss distributions.