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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.

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File URL: http://mpra.ub.uni-muenchen.de/1940/
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Bibliographic Info

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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Keywords: Coherent risk measure; distortion function; Spectral measures; Risk Aversion Function;

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  1. C. Gourieroux & J.P. Laurent & O. Scaillet, 2000. "Sensitivity analysis of values at risk," THEMA Working Papers 2000-04, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  2. Hurlimann, Werner, 2001. "Distribution-free comparison of pricing principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 351-360, June.
  3. 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.
  4. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  5. Schweizer, Martin, 2001. "From actuarial to financial valuation principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 31-47, February.
  6. John Cotter & Kevin Dowd, 2011. "Extreme Spectral Risk Measures: An Application to Futures Clearinghouse Margin Requirements," Working Papers 200516, Geary Institute, University College Dublin.
  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. repec:fth:inseep:2000-05 is not listed on IDEAS
  9. 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.
  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. Henryk Gzyl & Silvia Mayoral, . "Determination of Risk Pricing Measures from Market Prices of Risk," Faculty Working Papers 03/07, School of Economics and Business Administration, University of Navarra.

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