After VaR: The Theory, Estimation, and Insurance Applications of Quantile-Based Risk Measures

We discuss a number of quantile-based risk measures (QBRMs) that have recently been developed in the financial risk and actuarial/insurance literatures. The measures considered include the Value-at-Risk (VaR), coherent risk measures, spectral risk measures, and distortion risk measures. We discuss and compare the properties of these different measures, and point out that the VaR is seriously flawed. We then discuss how QBRMs can be estimated, and discuss some of the many ways they might be applied to insurance risk problems. These applications are typically very complex, and this complexity means that the most appropriate estimation method will often be some form of stochastic simulation. for many helpful discussions, and thank the editor, Pat Brockett, and two referees for helpful comments on an earlier draft. Dowd's contribution to this article was carried out under the auspices of an ESRC research fellowship on 'risk measurement in financial institutions' (RES-000-27-0014), and he thanks the ESRC for their financial support.