Discussion on: “Asymptotic analysis of multivariate tail conditional expectations”. (English) Zbl 1412.60076

Discussion to L. Zhu and H. Li [ibid. 16, No. 3, 350–363 (2012; Zbl 1291.60108)].


60G70 Extreme value theory; extremal stochastic processes
91B30 Risk theory, insurance (MSC2010)


Zbl 1291.60108


Full Text: DOI


[1] Artzner, P.; Delbaen, F.; Eber, J. M.; Heath, D., Coherent Measures of Risk, Mathematical Finance, 9, 203-228, (1999) · Zbl 0980.91042
[2] Asimit, A. V.; Furman, E.; Tang, Q.; Vernic, R., Asymptotics for Risk Capital Allocations Based on Conditional Tail Expectation, Insurance: Mathematics and Economics, 49, 3, 310-324, (2011) · Zbl 1228.91029
[3] Dhaene, J.; Henrard, L.; Landsman, Z.; Vandendorpe, A.; Vanduffel, S., Some Results on the CTE-Based Capital Allocation Rule, Insurance: Mathematics and Economics, 42, 855-863, (2008) · Zbl 1152.91577
[4] Dhaene, J.; Laeven, R. J. A.; Vanduffel, S.; Darkiewicz, G.; Goovaerts, M. J., Can a Coherent Risk Measure Be Too Subadditive?, Journal of Risk and Insurance, 75, 2, 365-386, (2004)
[5] Dhaene, J.; Vanduffel, S.; Tang, Q.; Goovaerts, M. J.; Kaas, R.; Vyncke, D., Risk Measures and Comonotonicity: A Review, Stochastic Models, 22, 573-606, (2006) · Zbl 1159.91403
[6] Fang, K. T.; Kotz, S.; Ng, K. W., Symmetric Multivariate and Related Distributions, (1990), London: Chapman & Hall, London
[7] Landsman, Z.; Valdez, E., Tail Conditional Expectations for Elliptical Distributions, North American Actuarial Journal, 7, 4, 55-71, (2002) · Zbl 1084.62512
[8] Landsman, Z.; Vanduffel, S., Bounds for Some Sums of Random Variables, Statistics & Probability Letters, 81, 3, 382-391, (2011) · Zbl 1207.62119
[9] Li, H.; Sun, Y., Tail Dependence for Heavy-Tailed Scale Mixtures of Multivariate Distributions, Journal of Applied Probability, 46, 925-937, (2009) · Zbl 1179.62076
[10] Mainik, G.; Rüschendorf, L., On Optimal Portfolio Diversification with Respect to Extreme Risks, Finance and Stochastics, 14, 4, 593-623, (2010) · Zbl 1226.91069
[11] McNeil, A. J.; Frey, R.; Embrechts, P., Quantitative Risk Management: Concepts, Techniques and Tools, (2005), PrincetonNJ: Princeton University Press, PrincetonNJ · Zbl 1089.91037
[12] Puccetti, G.; Rüschendorf, L., Asymptotic Equivalence of Conservative VaR- and ES-Based Capital Charges, (2012)
[13] Vanduffel, S.; Shang, Z.; Henrard, L.; Dhaene, J.; Valdez, E., Analytic Bounds and Approximations for Annuities and Asian Options, Insurance: Mathematics and Economics, 42, 3, 1109-1117, (2008) · Zbl 1141.91550
[14] Wang, S., Premium Calculation by Transforming the Layer Premium Density, ASTIN Bulletin, 26, 71-92, (1996)
[15] Wang, S.; Young, V., Ordering Risks: Expected Utility versus Yaari’s Dual Theory of Choice under Risk, Insurance: Mathematics & Economics, 22, 145-162, (1998) · Zbl 0907.90102
[16] Wirch, J. L.; Hardy, M. R., Ordering of Risk Measures for Capital Adequacy, (2000), Institute of Insurance and Pension Research, University of Waterloo
[17] Yaari, M. E., The Dual Theory of Choice under Risk, Econometrica, 55, 95-115, (1987) · Zbl 0616.90005
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