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

Kevin Dowd · David P. Blake

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Probability and Risk Models Insurance and Financial Risk Management Risk and Portfolio Optimization

Abstract

Abstract 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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References

1999Coherent Measures of Risk 1999An Introduction to Copulas 1997Modelling Extremal Events 2002Conditional value-at-risk for general loss distributions 2001Valuing American Options by Simulation: A Simple Least-Squares Approach 1998Evaluating Interval Forecasts 1995Techniques for Verifying the Accuracy of Risk Measurement Models 1987The Dual Theory of Choice under Risk

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