On the Expansion of Risk Pooling

Risk pooling has become an increasingly critical tool for managing risks among corporations, institutions, states, and nations, with examples including multinational pooling, decentralized insurance schemes, catastrophe risk pooling, and burden sharing for nuclear accidents. Although there has been a rich literature on such practices, little is known from a theoretical viewpoint regarding the operational strategies of risk pools and, in particular, on issues about the effect of a pool’s expansion on each existing member’s welfare. This paper is the first to explore these issues by establishing different notions of consensus for the expansion of a risk pool: strong consensus, where both existing members and new candidates improve their risk measures due to the pool’s expansion, and weak consensus, which refers to the willingness of existing members to remain in the pool. Under optimal risk sharing for each pool, we show that its properties regarding expansion’s effects depend strongly on the underlying pricing rule. For instance, only with risk-adjusted equilibrium pricing are existing members willing to accept highly risky new members, whereas simple linear pricing excludes such members from the pool. Additionally, the impact of exogenous reinsurance on consensus is analyzed under both pricing rules. The established framework offers valuable managerial insights and policy implications, which we illustrate through two indicative case studies based on real data. This paper was accepted by Agostino Capponi, finance. Funding: Financial support from the Tsinghua University School of Economics and Management [Research Grant 2023051001], the National Social Sciences Foundation of China [Major Grant 23&ZD178] is gratefully acknowledged, and the Tsinghua University Independent Research Grant [2024THZWYY02]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.06863 .