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On a relationship between distorted and spectral risk measures

  • Henryk, Gzyl
  • Silvia, Mayoral

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.

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File URL: https://mpra.ub.uni-muenchen.de/916/1/MPRA_paper_916.pdf
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File URL: https://mpra.ub.uni-muenchen.de/1940/1/MPRA_paper_1940.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 916.

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Date of creation: Nov 2006
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Handle: RePEc:pra:mprapa:916
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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. 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.
  3. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  4. Cotter, JOhn & Dowd, Kevin, 2006. "Extreme Spectral Risk Measures: An Application to Futures Clearinghouse Margin Requirements," MPRA Paper 3505, University Library of Munich, Germany.
  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. 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.
  8. Hurlimann, Werner, 2001. "Distribution-free comparison of pricing principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 351-360, June.
  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, 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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