Distortion Risk Measures and Economic Capital

Werner Hürlimann

North American Actuarial Journal, 2004, vol. 8, issue 1, 86-95

Abstract: To provide incentive for active risk management, it is argued that a sound coherent distortion risk measure should preserve some higher degree stop-loss orders, at least the degree-three convex order. Such risk measures are called tail-preserving risk measures. It is shown that, under some common axioms and other plausible conditions, a tail-preserving coherent distortion risk measure identifies necessarily with the Wang right-tail measure or the expected value measure. This main result is applied to derive an optimal economic capital formula.

Date: 2004
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DOI: 10.1080/10920277.2004.10596130

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