Multi-period Peer-to-Peer Risk Sharing

Abstract

Risk sharing has been practiced in various forms in the financial industry. This paper proposes a multi-period risk-sharing mechanism for a group of participants. The design of risk-sharing strategies is based on mean-variance optimizations of participants' terminal reserves. Such a framework builds a connection between mean-variance optimization for portfolio selection 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 in this work the peer-to-peer (P2P) network for risk sharing. Assuming that multivariate losses are independent 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. We also consider the P2P risk sharing in the dynamic versus the static settings. Furthermore, we study the impact of financial fairness on various risk sharing strategies and their long term limits. The paper provides numerical illustrations of the key research findings.

Keywords: Risk sharing; peer-to-peer insurance; mean-variance optimization; multi-period model; catastrophe risk pooling

JEL Classification: G22;