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A note on additive risk measures in rank-dependent utility

  • Goovaerts, Marc J.
  • Kaas, Rob
  • Laeven, Roger J.A.

This note proves that risk measures obtained by applying the equivalent utility principle in rank-dependent utility are additive if and only if the utility function is linear or exponential and the probability weighting (distortion) function is the identity.

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File URL: http://www.sciencedirect.com/science/article/B6V8N-5051PBW-1/2/62de7d62878adaafc2b419ffd327905b
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Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 47 (2010)
Issue (Month): 2 (October)
Pages: 187-189

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Handle: RePEc:eee:insuma:v:47:y:2010:i:2:p:187-189
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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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. Denuit Michel & Dhaene Jan & Goovaerts Marc & Kaas Rob & Laeven Roger, 2006. "Risk measurement with equivalent utility principles," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 25, July.
  3. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  4. Heilpern, S., 2003. "A rank-dependent generalization of zero utility principle," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 67-73, August.
  5. repec:dgr:uvatin:20040030 is not listed on IDEAS
  6. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  7. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  8. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  9. Gerber, Hans U., 1985. "On additive principles of zero utility," Insurance: Mathematics and Economics, Elsevier, vol. 4(4), pages 249-251, October.
  10. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A. & Tang, Qihe, 2004. "A comonotonic image of independence for additive risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 581-594, December.
  11. repec:dgr:uvatin:2004030 is not listed on IDEAS
  12. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
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