Multiperiod peer-to-peer risk sharing

Risk sharing has been practiced in various forms in the financial industry. This paper is the first to study both dynamic and static risk-sharing mechanisms for a group of participants over multiple periods. The design of risk-sharing strategies is based on the Pareto optimization of quadratic utilities of participants' reserves. Such a framework builds a connection between portfolio optimization in the finance literature and that for risk sharing in the insurance literature. Building on the most common form of reinsurance-pro rata treaties, we propose a peer-to-peer (P2P) network for risk sharing. Assuming independent multivariate losses over time, we find that the optimal risk-sharing allocation exhibits a three-component structure with the long-term limit and two correction terms. This allows us to show convergence of the risk-sharing solution and the ratios of long-term reserves. Furthermore, we study the impact of actuarial fairness on various risk-sharing strategies and their long-term limits.