We investigate the benefits of risk pooling for the policyholders of stock insurance companies under different solvency standards. Using second-degree stochastic dominance, we document that the utility of risk-averse policyholders is increasing in the pool size if the equity capital is proportional to the premiums written. To the contrary, an increase in the pool size can reduce the policyholders' utility if the equity capital is determined using the Value-at-Risk (VaR). We show that pooling with a larger number of risks is also beneficial for all risk-averse policyholders under a VaR-based regulation if the pool satisfies an excess tail risk restriction. Our analysis provides new insights for the design of solvency standards and reveals a potential disadvantage of risk-based capital requirements for policyholders.

Markus Huggenberger, Peter Albrecht

Dec 2022