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On a relationship between distorted and spectral risk measures

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  • 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.

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Bibliographic Info

Paper provided by School of Economics and Business Administration, University of Navarra in its series Faculty Working Papers with number 15/06.

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Length: 16 pages
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Publication status: Forthcoming, Revista Economía Financiera
Handle: RePEc:una:unccee:wp1506

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Web page: http://www.unav.es/facultad/econom

Related research

Keywords: Coherent risk measure; Distortion function; Spectral measures; risk aversion function.Spectral measu;

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References

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  1. Schweizer, Martin, 2001. "From actuarial to financial valuation principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 31-47, February.
  2. 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.
  3. Christian Gourieroux & J. P. Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Econometric Society World Congress 2000 Contributed Papers 0162, Econometric Society.
  4. 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.
  5. Cotter, JOhn & Dowd, Kevin, 2006. "Extreme Spectral Risk Measures: An Application to Futures Clearinghouse Margin Requirements," MPRA Paper 3505, University Library of Munich, Germany.
  6. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  7. Hurlimann, Werner, 2001. "Distribution-free comparison of pricing principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 351-360, June.
  8. 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.
  9. Christian Gourieroux & Jean-Paul Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Working Papers 2000-05, Centre de Recherche en Economie et Statistique.
  10. Acerbi Carlo & Simonetti Prospero, 2002. "Portfolio Optimization with Spectral Measures of Risk," Papers cond-mat/0203607, arXiv.org.
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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.

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