This paper considers a peer-to-peer (P2P) insurance scheme where the higher layer is transferred to a (re-)insurer and retained losses are distributed among participants according to the conditional mean risk sharing rule proposed by Denuit and Dhaene (2012). The global retention level of the pool of participants grows proportionally with their number. We study the asymptotic behavior of the individual retention levels, as well as individual cash-backs and stop-loss premiums, as the number of participants increases. The probability that the total loss hits the upper layer protected by the stop-loss treaty is also considered. The results depend on the proportional rate of increase of the global retention level with the number of participants, as well as on the existence of the Esscher transform of the losses brought to the pool.

本文考虑了一种点对点 (P2P) 保险方案，其中较高层转移到（再）保险公司，并根据 Denuit 和 Dhaene（2012）提出的条件平均风险分担规则在参与者之间分配保留损失. 参与者池的全球保留水平与他们的数量成正比增长。随着参与者数量的增加，我们研究了个人保留水平以及个人现金返还和止损溢价的渐近行为。还考虑了总损失达到止损条约保护的上层的概率。结果取决于全局保留水平与参与者数量的比例增加率，以及对池带来的损失的埃舍尔变换的存在。