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Correlation order, merging and diversification

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  • Dhaene, Jan
  • Denuit, Michel
  • Vanduffel, Steven

Abstract

We investigate the influence of the dependence between random losses on the shortfall and on the diversification benefit that arises from merging these losses. We prove that increasing the dependence between losses, expressed in terms of correlation order, has an increasing effect on the shortfall, expressed in terms of an appropriate integral stochastic order. Furthermore, increasing the dependence between losses decreases the diversification benefit. We also consider merging comonotonic losses and show that even in this extreme case a strictly positive diversification benefit will often arise.

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  • Dhaene, Jan & Denuit, Michel & Vanduffel, Steven, 2009. "Correlation order, merging and diversification," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 325-332, December.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:3:p:325-332
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    References listed on IDEAS

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    1. Zinoviy Landsman & Emiliano Valdez, 2003. "Tail Conditional Expectations for Elliptical Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 55-71.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Wang, Shaun & Dhaene, Jan, 1998. "Comonotonicity, correlation order and premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 235-242, July.
    4. Dhaene, J. & Henrard, L. & Landsman, Z. & Vandendorpe, A. & Vanduffel, S., 2008. "Some results on the CTE-based capital allocation rule," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 855-863, April.
    5. Dhaene, Jan & Goovaerts, Marc J., 1996. "Dependency of Risks and Stop-Loss Order1," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 201-212, November.
    6. J. Dhaene & R. J. A. Laeven & S. Vanduffel & G. Darkiewicz & M. J. Goovaerts, 2008. "Can a Coherent Risk Measure Be Too Subadditive?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 365-386, June.
    7. Stan Alink & Matthias Löwe & Mario V. Wüthrich, 2007. "Diversification for general copula dependence," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 446-465, November.
    8. Valdez, Emiliano A. & Dhaene, Jan & Maj, Mateusz & Vanduffel, Steven, 2009. "Bounds and approximations for sums of dependent log-elliptical random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 385-397, June.
    9. Kaas, R. & Dhaene, J. & Vyncke, D. & Goovaerts, M.J. & Denuit, M., 2002. "A Simple Geometric Proof that Comonotonic Risks Have the Convex-Largest Sum," ASTIN Bulletin, Cambridge University Press, vol. 32(1), pages 71-80, May.
    10. Muller, Alfred, 1997. "Stop-loss order for portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 219-223, December.
    11. Dhaene, J. & Goovaerts, M. J., 1997. "On the dependency of risks in the individual life model," Insurance: Mathematics and Economics, Elsevier, vol. 19(3), pages 243-253, May.
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    4. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
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    7. Ćmiel, Bogdan & Ledwina, Teresa, 2020. "Validation of association," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 55-67.

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