Optimal Risk-Sharing Across a Network of Insurance Companies

Abstract

Risk transfer is a key risk and capital management tool for insurance companies. Transferring risk between insurers is used to mitigate risk and manage capital re- quirements. We investigate risk transfer in the context of a network environment of insurers and consider capital costs and capital constraints at the level of individual insurance companies. We demonstrate that the optimisation of profitability across the network can be achieved through risk transfer. Considering only individual in- surance companies, there is no unique optimal solution and, a priori, it is not clear which solutions are fair. However, from a network perspective, we derive a unique fair solution in the sense of cooperative game theory. Implications for systemic risk are briefly discussed.

Keywords: risk transfer, risk-based capital, reinsurance, return optimisation, conditional expected shortfall

JEL Classification: G13, G22, D85, C57, C71