Multiperiod peer‐to‐peer risk sharing

Abstract

AbstractRisk 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.