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

Kevin Dowd and David Blake

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.

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