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A note on additive risk measures in rank-dependent utility

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

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/inca/505554

Related research

Keywords: Decision-making Measure of risk Premium principle Equivalent utility Rank-dependent utility Exponential utility Axiomatization Additivity;

References

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  1. Marc J. Goovaerts & Rob Kaas & Roger J.A. Laeven & Qihe Tang, 2004. "A Comonotonic Image of Independence for Additive Risk Measures," Tinbergen Institute Discussion Papers, Tinbergen Institute 04-030/4, Tinbergen Institute.
  2. Heilpern, S., 2003. "A rank-dependent generalization of zero utility principle," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 33(1), pages 67-73, August.
  3. Gerber, Hans U., 1985. "On additive principles of zero utility," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 4(4), pages 249-251, October.
  4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 571-87, May.
  5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 18(2), pages 141-153, April.
  6. Goovaerts, Marc J. & Laeven, Roger J.A., 2008. "Actuarial risk measures for financial derivative pricing," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 42(2), pages 540-547, April.
  7. 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, Elsevier, vol. 35(3), pages 581-594, December.
  8. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 3(4), pages 323-343, December.
  9. Denuit Michel & Dhaene Jan & Goovaerts Marc & Kaas Rob & Laeven Roger, 2006. "Risk measurement with equivalent utility principles," Statistics & Risk Modeling, De Gruyter, De Gruyter, vol. 24(1/2006), pages 25, July.
  10. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, Springer, vol. 5(4), pages 297-323, October.
  11. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 95-115, January.
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Citations

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Cited by:
  1. Jaume Belles-Sampera & José M. Merigó & Montserrat Guillén & Miguel Santolino, 2012. "The connection between distortion risk measures and ordered weighted averaging operators," IREA Working Papers, University of Barcelona, Research Institute of Applied Economics 201201, University of Barcelona, Research Institute of Applied Economics, revised Jan 2012.
  2. Kaluszka, Marek & Krzeszowiec, Michał, 2013. "On iterative premium calculation principles under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 52(3), pages 435-440.
  3. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "Decision principles derived from risk measures," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 47(3), pages 294-302, December.
  4. Kaluszka, Marek & Krzeszowiec, Michał, 2012. "Pricing insurance contracts under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 50(1), pages 159-166.
  5. Goovaerts, Marc & Linders, Daniël & Van Weert, Koen & Tank, Fatih, 2012. "On the interplay between distortion, mean value and Haezendonck–Goovaerts risk measures," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 51(1), pages 10-18.
  6. Marek Kałuszka & Michał Krzeszowiec, 2013. "Iteracyjność składek ubezpieczeniowych w ujęciu teorii skumulowanej perspektywy i teorii nieokreśloności," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, Warsaw School of Economics, Collegium of Economic Analysis, issue 31, pages 45-56.

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