Shapley risk sharing in peer-to-peer insurance

Peer-to-peer (P2P) insurance is an innovative model that leverages digital technology to connect individuals with similar insurance needs, forming a pool to share risks. This paper introduces a P2P insurance framework in which participants pay an ex-ante contribution determined by the Shapley value, where Value-at-Risk of the difference between the expected and realized total loss of the network (i.e., the Profit and Loss) is used as the risk measure. Under standard assumptions commonly used in non-life insurance for the aggregate claim amount, we derive closed-form expressions for the Shapley value. The model includes a cashback mechanism to ensure that all participants contribute equally to covering realized losses. We demonstrate the practical implementation of the model by applying it to a portfolio of motor other damage insurance policies.