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On a relationship between distorted and spectral risk measures

Author

Listed:
  • Henryk Gzyl

    (Centro de Finanzas, IESA)

  • Silvia Mayoral

    (Universidad de Navarra)

Abstract

We study the relationship between two widely used risk measures, spectral measures and distortion risk measures. In both cases, the risk measure can be thought of as a re-weighting of some initial distribution. We prove that spectral risk measures are equivalent to distorted risk pricing measures, or equivalently, spectral risk functions are equivalent to distortion functions. Besides, we prove that distorted measures are absolutely continuous with respect to the original measure. This allows us to find a link between the risk measures based on relative entropy and spectral risk measures or measures based on distortion risk functions.

Suggested Citation

  • 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.
    • Handle: RePEc:una:unccee:wp1506
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    References listed on IDEAS

    as
    1. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
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    7. Acerbi Carlo & Simonetti Prospero, 2002. "Portfolio Optimization with Spectral Measures of Risk," Papers cond-mat/0203607, arXiv.org.
    8. Schweizer, Martin, 2001. "From actuarial to financial valuation principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 31-47, February.
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    Cited by:

    1. Liu, Yangyang & Zhou, Jiangxin & Zhou, Qihui & Liu, Chuanquan & Yu, Feng, 2023. "Bidding strategy of integrated energy system considering decision maker’s subjective risk aversion," Applied Energy, Elsevier, vol. 341(C).
    2. Gzyl, Henryk & Mayoral, Silvia, 2008. "Determination of risk pricing measures from market prices of risk," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 437-443, December.

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    JEL classification:

    • J13 - Labor and Demographic Economics - - Demographic Economics - - - Fertility; Family Planning; Child Care; Children; Youth

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