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On a relationship between distorted and spectral risk measures

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  • Henryk, Gzyl
  • Silvia, Mayoral

Abstract

We study the relationship between two widely used risk measures, the spectral measures and the 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 related to distortion functions. Besides that we prove that distorted measures are absolutely continuous with respect to the original measure.

Suggested Citation

  • Henryk, Gzyl & Silvia, Mayoral, 2006. "On a relationship between distorted and spectral risk measures," MPRA Paper 916, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:916
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    References listed on IDEAS

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    1. Goovaerts, Marc J. & Laeven, Roger J.A., 2008. "Actuarial risk measures for financial derivative pricing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 540-547, April.
    2. Cotter, John & Dowd, Kevin, 2006. "Extreme spectral risk measures: An application to futures clearinghouse margin requirements," Journal of Banking & Finance, Elsevier, vol. 30(12), pages 3469-3485, December.
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    5. Acerbi Carlo & Simonetti Prospero, 2002. "Portfolio Optimization with Spectral Measures of Risk," Papers cond-mat/0203607, arXiv.org.
    6. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
    7. 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.
    8. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    9. Schweizer, Martin, 2001. "From actuarial to financial valuation principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 31-47, February.
    10. Werner Hürlimann, 2004. "Distortion Risk Measures and Economic Capital," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(1), pages 86-95.
    11. Hurlimann, Werner, 2001. "Distribution-free comparison of pricing principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 351-360, June.
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    Cited by:

    1. 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.
    2. 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).

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    More about this item

    Keywords

    Coherent risk measure; distortion function; Spectral measures; Risk Aversion Function;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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