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Equivalent distortion risk measures on moment spaces

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  • Cornilly, Dries
  • Vanduffel, Steven

Abstract

We show that maximizing distortion risk measures over the set of distributions with given mean is equivalent to maximizing their concave counterpart. In the case of Value-at-Risk and Tail Value-at-Risk the equivalence also holds when adding information on higher moments.

Suggested Citation

  • Cornilly, Dries & Vanduffel, Steven, 2019. "Equivalent distortion risk measures on moment spaces," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 187-192.
    • Handle: RePEc:eee:stapro:v:146:y:2019:i:c:p:187-192
    DOI: 10.1016/j.spl.2018.11.021
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    References listed on IDEAS

    as
    1. Carole Bernard & Michel Denuit & Steven Vanduffel, 2018. "Measuring Portfolio Risk Under Partial Dependence Information," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(3), pages 843-863, September.
    2. Bernard, Carole & Vanduffel, Steven, 2015. "A new approach to assessing model risk in high dimensions," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 166-178.
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    7. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel, 2017. "Value-at-Risk Bounds With Variance Constraints," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 923-959, September.
    8. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
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    10. Jonathan Yu-Meng Li, 2016. "Closed-form solutions for worst-case law invariant risk measures with application to robust portfolio optimization," Papers 1609.04065, arXiv.org.
    11. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Ruodu Wang, 2017. "Risk bounds for factor models," Finance and Stochastics, Springer, vol. 21(3), pages 631-659, July.
    12. Jun Cai & Haiyan Liu & Ruodu Wang, 2018. "Asymptotic Equivalence Of Risk Measures Under Dependence Uncertainty," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 29-49, January.
    13. Paul Embrechts & Bin Wang & Ruodu Wang, 2015. "Aggregation-robustness and model uncertainty of regulatory risk measures," Finance and Stochastics, Springer, vol. 19(4), pages 763-790, October.
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