Discussion on “Asymptotic Analysis of Multivariate Tail Conditional Expectations,” by Li Zhu and Haijun Li, Volume 16(3)

REFERENCES

• Artzner , P. , Delbaen , F. , Eber , J. M. and Heath , D. 1999 . Coherent Measures of Risk . Mathematical Finance , 9 : 203 – 228 .
   Web of Science ®Google Scholar
• Asimit , A. V. , Furman , E. , Tang , Q. and Vernic , R. 2011 . Asymptotics for Risk Capital Allocations Based on Conditional Tail Expectation . Insurance: Mathematics and Economics , 49 ( 3 ) : 310 – 324 .
   Web of Science ®Google Scholar
• Dhaene , J. , Henrard , L. , Landsman , Z. , Vandendorpe , A. and Vanduffel , S. 2008 . Some Results on the CTE-Based Capital Allocation Rule . Insurance: Mathematics and Economics , 42 : 855 – 863 .
   Web of Science ®Google Scholar
• Dhaene , J. , Laeven , R. J. A. , Vanduffel , S. , Darkiewicz , G. and Goovaerts , M. J. 2004 . Can a Coherent Risk Measure Be Too Subadditive? . Journal of Risk and Insurance , 75 ( 2 ) : 365 – 386 .
   Google Scholar
• Dhaene , J. , Vanduffel , S. , Tang , Q. , Goovaerts , M. J. , Kaas , R. and Vyncke , D. 2006 . Risk Measures and Comonotonicity: A Review . Stochastic Models , 22 : 573 – 606 .
   Web of Science ®Google Scholar
• Fang , K. T. , Kotz , S. and Ng , K. W. 1990 . Symmetric Multivariate and Related Distributions , London : Chapman & Hall .
   Google Scholar
• Landsman , Z. and Valdez , E. 2002 . Tail Conditional Expectations for Elliptical Distributions . North American Actuarial Journal , 7 ( 4 ) : 55 – 71 .
   Google Scholar
• Landsman , Z. and Vanduffel , S. 2011 . Bounds for Some Sums of Random Variables . Statistics & Probability Letters , 81 ( 3 ) : 382 – 391 .
   Google Scholar
• Li , H. and Sun , Y. 2009 . Tail Dependence for Heavy-Tailed Scale Mixtures of Multivariate Distributions . Journal of Applied Probability , 46 : 925 – 937 .
   Web of Science ®Google Scholar
• Mainik , G. and Rüschendorf , L. 2010 . On Optimal Portfolio Diversification with Respect to Extreme Risks . Finance and Stochastics , 14 ( 4 ) : 593 – 623 .
   Web of Science ®Google Scholar
• McNeil , A. J. , Frey , R. and Embrechts , P. 2005 . Quantitative Risk Management: Concepts, Techniques and Tools , Princeton , NJ : Princeton University Press .
   Google Scholar
• Puccetti , G. and Rüschendorf , L. 2012 . Asymptotic Equivalence of Conservative VaR- and ES-Based Capital Charges . Preprint, available at https://docs.google.com/file/d/0B5jPd-_e0JLfSVRXekd1QUxLUG8/edit
   Google Scholar
• Vanduffel , S. , Shang , Z. , Henrard , L. , Dhaene , J. and Valdez , E. 2008 . Analytic Bounds and Approximations for Annuities and Asian Options . Insurance: Mathematics and Economics , 42 ( 3 ) : 1109 – 1117 .
   Web of Science ®Google Scholar
• Wang , S. 1996 . Premium Calculation by Transforming the Layer Premium Density . ASTIN Bulletin , 26 : 71 – 92 .
   Google Scholar
• Wang , S. and Young , V. 1998 . Ordering Risks: Expected Utility versus Yaari's Dual Theory of Choice under Risk . Insurance: Mathematics & Economics , 22 : 145 – 162 .
   Web of Science ®Google Scholar
• Wirch , J. L. and Hardy , M. R. 2000 . “ Ordering of Risk Measures for Capital Adequacy ” . Institute of Insurance and Pension Research, University of Waterloo . Research Report 00-03
   Google Scholar
• Yaari , M. E. 1987 . The Dual Theory of Choice under Risk . Econometrica , 55 : 95 – 115 .
   Web of Science ®Google Scholar