Optimal Risk Pooling of Peer-to-Peer Insurance

Peer-to-peer insurance models combine insurer's underwriting with peers' risk sharing. This paper presents a mathematical formulation of two emerging peer-to-peer insurance models: the individual-covered model and the group-covered model, and establishes their equivalence for a homogeneous participant pool. Both models involve a two-layered risk allocation approach: the first layer covers losses below the deductible and is distributed among the participants, while the second layer addresses losses that surpass the risk-bearing capacity of the pool and are assumed by an insurer. Furthermore, we provide a theoretical analysis of the optimal level of risk pooling in terms of the deductible in peer-to-peer insurance, exploring its existence, closed-form expression, and associated properties