**DISCUSSION PAPER PI-0603**

**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.