Optimal Reinsurance Arrangements Under Tail Risk Measures

Regulatory authorities demand insurance companies to control the risks by imposing stringent risk management policies. This article investigates the insurance company’s optimal risk management strategy subject to regulator’s risk measure constraints. We first design the optimal reinsurance contracts under different tail risk measures. Then we analyze the impact of the regulators’ requirements on the way insurers and reinsurers share risks. Our results underline some adverse incentives when requirements are based on the Value-at-Risk or the Conditional Tail Expectation risk measure. Our findings confirm recent empirical studies (for instance Froot (2001)) which show that insurers do not often purchase coverage for high layers of risk. Alternative risk measure might be more appropriate to request insurance companies to concentrate on large amount of risk. Finally we provide alternative risk transfer mechanisms on the capital market.