Some results on the CTE-based capital allocation rule
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.
Year of publication: |
2008
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Authors: | Dhaene, J. ; Henrard, L. ; Landsman, Z. ; Vandendorpe, A. ; Vanduffel, S. |
Published in: |
Insurance: Mathematics and Economics. - Elsevier, ISSN 0167-6687. - Vol. 42.2008, 2, p. 855-863
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Publisher: |
Elsevier |
Saved in:
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