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A Comonotonic Image of Independence for Additive Risk Measures

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Author Info

  • Marc J. Goovaerts

    () (Faculty of Economics and Econometrics, Universiteit van Amsterdam, and Cath. University of Leuven, Center for Risk and Insurance Studies)

  • Rob Kaas

    (Faculty of Economics and Econometrics, Universiteit van Amsterdam)

  • Roger J.A. Laeven

    () (Faculty of Economics and Econometrics, Universiteit van Amsterdam)

  • Qihe Tang

    (Faculty of Economics and Econometrics, Universiteit van Amsterdam)

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

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 04-030/4.

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Date of creation: 15 Mar 2004
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Handle: RePEc:dgr:uvatin:20040030

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Related research

Keywords: Risk measures; Additivity; Exponential order; Laplace transform order; Esscher transform; Comonotonicity;

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References

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  1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  2. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  3. 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, vol. 31(1), pages 3-33, August.
  4. Denuit, Michel, 2001. "Laplace transform ordering of actuarial quantities," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 83-102, August.
  5. 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, vol. 31(2), pages 133-161, October.
  6. Goovaerts, Marc & Kaas, R. & Dhaene, Jan & Tang, Q., 2003. "A unified approach to generate risk measures," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/200990, Katholieke Universiteit Leuven.
  7. Van Heerwaarden, A. E. & Kaas, R. & Goovaerts, M. J., 1989. "Properties of the Esscher premium calculation principle," Insurance: Mathematics and Economics, Elsevier, vol. 8(4), pages 261-267, December.
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