Capital, Systemic Risk, Insurance Prices and Regulation

We develop a uni ed equilibrium model of competitive insurance markets that incorporates the demand and supply of insurance as well as insurers' asset and liability risks. Insurers' assets may be exposed to both idiosyncratic and systemic shocks. We obtain new insights into the relationship between insurance premia and insurers' internal capital that potentially reconcile the con icting predictions of previous theories that investigate the relation using partial equilibrium frameworks. Equilibrium e ects lead to a non-monotonic U-shaped relation between insurance price and internal capital. We study the e ects of systemic risk on the optimal asset and liquidity management by insurers as well as risk-sharing between insurers and insurees. In the rst-best benchmark scenario, we show that, when systemic risk is low, both insurees and insurers hold no liquidity reserves, insurees are fully insured, and insurers bear all the systemic risk. When systemic risk takes intermediate values, both insurees and insurers still hold no liquidity reserves, but insurees partially share systemic risk with insurers. When systemic risk is high, however, both insurees and insurers hold some liquidity reserves, and insurees partially share systemic risk with insurers. The rst best asset and liquidity management policies as well as the systemic risk allocation can be implemented through a regulatory intervention policy that combines a minimum liquidity requirement, ex post taxation contingent on the aggregate state, comprehensive insurance policies, and reinsurance. We also provide implications for the solvency regulation of insurers facing systemic risk.