Abstract：Peer-to-peer insurance models, that jointly incorporate the forms of centralized insurer's underwriting and decentralized peers' risk sharing, are emerging. Under these innovative risk sharing forms, the risk is separated into two layers: the first below-deductible part is shared within a community, and the second above-deductible loss, exceeding the community’s risk-bearing capacity, is covered by an insurer. In this paper, we mathematically formalize two existing peer-to-peer insurance models: the individual-and group-covered models. From the perspective of risk-averse participants, we investigate the existence, closed-form expression, and properties of optimal deductible, the primary feature of peer-to-peer insurance.