Compensation-based risk-sharing

This paper studies the mathematical problem of allocating payouts (compensations) in an endowment contingency fund using a risk-sharing rule that satisfies full allocation. Besides the participants, an administrator manages the fund by collecting ex-ante contributions to establish the fund and distributing ex-post payouts to members. Two types of administrators are considered. An 'active' administrator both invests in the fund and receives the payout of the fund when no participant receives a payout. A 'passive' administrator performs only administrative tasks and neither invests in nor receives a payout from the fund. We analyze the actuarial fairness of both compensation-based risk-sharing schemes and provide general conditions under which fairness is achieved. The results extend earlier work by Denuit and Robert (2025) and Dhaene and Milevsky (2024), who focused on payouts based on Bernoulli distributions, by allowing for general non-negative loss distributions.