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

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. Copyright The Journal of Risk and Insurance, 2006.

Value-at-Risk and Conditional Value-at-Risk Minimization for Hazardous Materials Routing

“…CVaR is a risk measure that is a computationally tractable and coherent alternative to VaR. The notion of CVaR is closely related to the notions of Expected Tail Loss, Tail Conditional Expectation, Tail VaR, Average VaR, Worst Conditional Expectation, or Expected Shortfall (Rockafellar and Uryasev, 2000;Dowd and Blake, 2006). Unlike VaR, CVaR provides an optimization framework with convexity.…”

“…Despite its wide usage, VaR has been criticized as a risk measure due to the fact that it is not a coherent risk measure (Artzner et al, 1999;Dowd and Blake, 2006) and it might lead to inaccurate perception of risk (Nocera, 2009;Einhorn, 2008). It is claimed that VaR cuts off and ignores what is happening in the tail of the distribution as shown in Figure 1.…”

“…Due to the fact that accident probabilities are very small in each road segment with high consequences at the same time, using VaR as a risk measure may result the cut off of that particular road segment. Both VaR and CVaR are quantile-based risk measures (Dowd and Blake, 2006). Their main difference is the fact that CVaR accounts for the distribution in the long tail whereas VaR does not.…”

EVA/RAROC vs. MCEV Earnings: A Unification Approach

“…26 See Porteous and Tapadar (2008). 27 See, for example, Dowd and Blake (2006). 28 See Cummins (2000).…”

Risk Measures and Capital Requirements: A Critique of the Solvency II Approach

“…6 Cf. Basak and Shapiro (2001); Alexander and Baptista (2006); Dowd and Blake (2006). 7 Cf., among others, Cuoco and Liu (2006); Leippold et al (2006).…”