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A comonotonic image of independence for additive risk measures

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

Abstract

This paper presents a new axiomatic characterization of risk measures that are additive for independent random variables. In contrast to previous work, we include an axiom that guarantees monotonicity of the risk measure. Furthermore, the axiom of additivity for independent random variables is related to an axiom of additivity for comonotonic random variables. The risk measure characterized can be regarded as a mixed exponential premium.

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Bibliographic Info

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 35 (2004)
Issue (Month): 3 (December)
Pages: 581-594

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Handle: RePEc:eee:insuma:v:35:y:2004:i:3:p:581-594

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

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  1. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 31(1), pages 3-33, August.
  2. Van Heerwaarden, A. E. & Kaas, R. & Goovaerts, M. J., 1989. "Properties of the Esscher premium calculation principle," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 8(4), pages 261-267, December.
  3. Denuit, Michel, 2001. "Laplace transform ordering of actuarial quantities," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 29(1), pages 83-102, August.
  4. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  5. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 95-115, January.
  6. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 31(2), pages 133-161, October.
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Cited by:
  1. Kaluszka, M. & Laeven, R.J.A. & Okolewski, A., 2012. "A note on weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 51(2), pages 379-381.
  2. 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.
  3. Henryk Gzyl & Silvia Mayoral, . "Determination of Risk Pricing Measures from Market Prices of Risk," Faculty Working Papers, School of Economics and Business Administration, University of Navarra 03/07, School of Economics and Business Administration, University of Navarra.
  4. Lau, John W. & Siu, Tak Kuen, 2008. "On option pricing under a completely random measure via a generalized Esscher transform," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 43(1), pages 99-107, August.
  5. Kijima, Masaaki & Muromachi, Yukio, 2008. "An extension of the Wang transform derived from Bühlmann's economic premium principle for insurance risk," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 42(3), pages 887-896, June.
  6. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted risk capital allocations," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 43(2), pages 263-269, October.
  7. Paola Ferretti & Antonella Campana, 2011. "XL reinsurance with reinstatements and initial premium feasibility in exchangeability hypothesis," Working Papers, Department of Economics, University of Venice "Ca' Foscari" 2011_14, Department of Economics, University of Venice "Ca' Foscari".
  8. Li, Peng & Lim, Andrew E.B. & Shanthikumar, J. George, 2010. "Optimal risk transfer for agents with germs," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 47(1), pages 1-12, August.
  9. Acciaio, Beatrice & Svindland, Gregor, 2009. "Optimal risk sharing with different reference probabilities," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 44(3), pages 426-433, June.
  10. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "A note on additive risk measures in rank-dependent utility," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 47(2), pages 187-189, October.
  11. 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.
  12. Badescu, Alex & Elliott, Robert J. & Siu, Tak Kuen, 2009. "Esscher transforms and consumption-based models," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 45(3), pages 337-347, December.
  13. Wu, Xianyi & Zhou, Xian, 2006. "A new characterization of distortion premiums via countable additivity for comonotonic risks," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 38(2), pages 324-334, April.
  14. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 42(1), pages 459-465, February.
  15. 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.
  16. Labuschagne, Coenraad C.A. & Offwood, Theresa M., 2010. "A note on the connection between the Esscher-Girsanov transform and the Wang transform," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 47(3), pages 385-390, December.
  17. He, Kun & Hu, Mingshang & Chen, Zengjing, 2009. "The relationship between risk measures and choquet expectations in the framework of g-expectations," Statistics & Probability Letters, Elsevier, Elsevier, vol. 79(4), pages 508-512, February.
  18. Liew, Chuin Ching & Siu, Tak Kuen, 2010. "A hidden Markov regime-switching model for option valuation," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 47(3), pages 374-384, December.
  19. Kaluszka, Marek & Krzeszowiec, Michał, 2012. "Pricing insurance contracts under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 50(1), pages 159-166.
  20. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2009. "Optimal reinsurance with general risk measures," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 44(3), pages 374-384, June.
  21. Corradini, M. & Gheno, A., 2009. "Incomplete financial markets and contingent claim pricing in a dual expected utility theory framework," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 45(2), pages 180-187, October.
  22. Stadje, Mitja, 2010. "Extending dynamic convex risk measures from discrete time to continuous time: A convergence approach," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 47(3), pages 391-404, December.

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