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Some results on the CTE-based capital allocation rule

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  • Dhaene, J.
  • Henrard, L.
  • Landsman, Z.
  • Vandendorpe, A.
  • Vanduffel, S.

Abstract

Tasche [Tasche, D., 1999. Risk contributions and performance measurement. Working paper, Technische Universität München] introduces a capital allocation principle where the capital allocated to each risk unit can be expressed in terms of its contribution to the conditional tail expectation (CTE) of the aggregate risk. Panjer [Panjer, H.H., 2002. Measurement of risk, solvency requirements and allocation of capital within financial conglomerates. Institute of Insurance and Pension Research, University of Waterloo, Research Report 01-15] derives a closed-form expression for this allocation rule in the multivariate normal case. Landsman and Valdez [Landsman, Z., Valdez, E., 2002. Tail conditional expectations for elliptical distributions. North American Actuarial J. 7 (4)] generalize Panjer's result to the class of multivariate elliptical distributions. In this paper we provide an alternative and simpler proof for the CTE-based allocation formula in the elliptical case. Furthermore, we derive accurate and easy computable closed-form approximations for this allocation formula for sums that involve normal and lognormal risks.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:855-863
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    References listed on IDEAS

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    1. Landsman, Zinoviy & Tsanakas, Andreas, 2006. "Stochastic ordering of bivariate elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 488-494, March.
    2. Kaas, Rob & Dhaene, Jan & Goovaerts, Marc J., 2000. "Upper and lower bounds for sums of random variables," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 151-168, October.
    3. Zinoviy Landsman & Emiliano Valdez, 2003. "Tail Conditional Expectations for Elliptical Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 55-71.
    4. 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.
    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. Anderson, Dale N., 1992. "A multivariate Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 14(4), pages 333-336, July.
    7. Jan Dhaene & Andreas Tsanakas & Emiliano A. Valdez & Steven Vanduffel, 2012. "Optimal Capital Allocation Principles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(1), pages 1-28, March.
    8. Furman, Edward & Landsman, Zinoviy, 2005. "Risk capital decomposition for a multivariate dependent gamma portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 635-649, December.
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