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Beyond Value‐at‐Risk: GlueVaR Distortion Risk Measures

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  • Jaume Belles‐Sampera
  • Montserrat Guillén
  • Miguel Santolino

Abstract

We propose a new family of risk measures, called GlueVaR, within the class of distortion risk measures. Analytical closed‐form expressions are shown for the most frequently used distribution functions in financial and insurance applications. The relationship between GlueVaR, value‐at‐risk, and tail value‐at‐risk is explained. Tail subadditivity is investigated and it is shown that some GlueVaR risk measures satisfy this property. An interpretation in terms of risk attitudes is provided and a discussion is given on the applicability in nonfinancial problems such as health, safety, environmental, or catastrophic risk management.

Suggested Citation

  • Jaume Belles‐Sampera & Montserrat Guillén & Miguel Santolino, 2014. "Beyond Value‐at‐Risk: GlueVaR Distortion Risk Measures," Risk Analysis, John Wiley & Sons, vol. 34(1), pages 121-134, January.
    • Handle: RePEc:wly:riskan:v:34:y:2014:i:1:p:121-134
    DOI: 10.1111/risa.12080
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    3. Cornilly, D. & Rüschendorf, L. & Vanduffel, S., 2018. "Upper bounds for strictly concave distortion risk measures on moment spaces," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 141-151.
    4. Boonen, Tim J. & Jiang, Wenjun, 2022. "A marginal indemnity function approach to optimal reinsurance under the Vajda condition," European Journal of Operational Research, Elsevier, vol. 303(2), pages 928-944.
    5. Vanda Tulli & Mauro Gallegati & Gerd Weinrich, 2019. "Financial conditions and supply decisions when firms are risk averse," Journal of Economics, Springer, vol. 128(3), pages 259-289, December.
    6. Eric Benhamou & Beatrice Guez & Nicolas Paris1, 2019. "Omega and Sharpe ratio," Papers 1911.10254, arXiv.org.
    7. Andreas Tsanakas & Pietro Millossovich, 2016. "Sensitivity Analysis Using Risk Measures," Risk Analysis, John Wiley & Sons, vol. 36(1), pages 30-48, January.
    8. Wei Wang & Huifu Xu, 2023. "Preference robust state-dependent distortion risk measure on act space and its application in optimal decision making," Computational Management Science, Springer, vol. 20(1), pages 1-51, December.
    9. Krężołek Dominik, 2016. "The Gluevar Risk Measure and Investor’s Attitudes to Risk–An Application to the Non-Ferrous Metals Market," Statistics in Transition New Series, Statistics Poland, vol. 17(2), pages 305-316, June.
    10. Ghossoub, Mario & Jiang, Wenjun & Ren, Jiandong, 2022. "Pareto-optimal reinsurance under individual risk constraints," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 307-325.

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