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Distortion Risk Measures and Economic Capital

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  • Werner Hürlimann

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.

Suggested Citation

  • Werner Hürlimann, 2004. "Distortion Risk Measures and Economic Capital," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(1), pages 86-95.
    • Handle: RePEc:taf:uaajxx:v:8:y:2004:i:1:p:86-95
    DOI: 10.1080/10920277.2004.10596130
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    Cited by:

    1. Henryk Gzyl & Silvia Mayoral, 2006. "On a relationship between distorted and spectral risk measures," Faculty Working Papers 15/06, School of Economics and Business Administration, University of Navarra.
    2. Saralees Nadarajah & Bo Zhang & Stephen Chan, 2014. "Estimation methods for expected shortfall," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 271-291, February.
    3. Lin, Feng & Peng, Liang & Xie, Jiehua & Yang, Jingping, 2018. "Stochastic distortion and its transformed copula," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 148-166.

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