Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - University of Rouen Normandy

Peer-to-peer (P2P) insurance promises lower costs and better alignment of interests by having small groups of policyholders directly share risk. Yet full pooling can destroy prevention incentives under moral hazard, while self-insurance sacrifices diversification. In this talk, we develop a unified mean–variance framework that endogenizes both the pooling matrix and the effort levels in one joint optimization. Under observable effort, we show the social-planner’s biconvex program reduces to a single linear fixed-point system—admitting closed-form solutions in the homogeneous case and a provably unique equilibrium in general. Under hidden effort, we cast the problem as a two-stage Stackelberg game: the platform first selects retention floors, then agents play a Nash effort game. Remarkably, in the independent-risk special case, this bilevel problem collapses to a single convex program. Numerical examples illustrate how optimal retention rules balance diversification and incentives, and how decentralized Nash outcomes diverge from Pareto efficiency. We conclude with design recommendations for next-generation P2P platforms and regulatory insights on retention-floor mandates.