Tail conditional moment for generalized skew-elliptical distributions

References

• C.J. Adcock, Z. Landsman, and T. Shushi, Stein’s Lemma for generalized skew-elliptical random vectors. Com. Stat. Meth. (2019). doi:https://doi.org/10.1080/03610926.2019.1678642.
   Google Scholar
• P. Artzner, F. Delbaen, J.M. Eber, and D. Heath, Coherent measures of risk. Math. Financ. 9 (1999), pp. 203–228.
   Web of Science ®Google Scholar
• A. Azzalini, Some properties of skew-symmetric distributions. Scand. J. Stat. 12 (1985), pp. 171–178.
   Web of Science ®Google Scholar
• A. Azzalini, and A. Capitanio, Statistical applications of the multivariate skew-normal distribution. J. Roy. Stat. Soci. Series B 61 (1999), pp. 579–602.
   Google Scholar
• A. Azzalini, and A. Dalla Valle, The multivariate skew-normal distribution. Biometrika 83 (1996), pp. 715–726.
   Web of Science ®Google Scholar
• M.D. Branco, and D.K. Dey, A general class of multivariate skew-elliptical distributions. J. Mult. Anal. 79 (2001), pp. 99–113.
   Web of Science ®Google Scholar
• H. Exton, Multiple Hypergeometric Functions and Applications, Ellis Horwood, Chichester, New York, 1976.
   Google Scholar
• K.T. Fang, S. Kotz, and K.W. Ng, Symmetric Multivariate and Related Distributions, Chapman and Hall, London, 1987.
   Google Scholar
• E. Furman, and Z. Landsman, Tail variance premium with applications for elliptical portfolio of risks. Aust. Bul. 36 (2006), pp. 433–462.
   Web of Science ®Google Scholar
• M. Galea, J.A. Díaz-García, and F. Vilca, Influence diagnostics in the capital asset pricing model under elliptical distributions. J. Appl. Stat. 35 (2008), pp. 179–192.
   Web of Science ®Google Scholar
• A.K. Gupta, and T. Varga, Elliptically Contoured Models in Statistics, Kluwer Academic Publisher, Dordrecht, 1993.
   Google Scholar
• K. Ignatieva, and Z. Landsman, Conditional tail risk measures for the skewed generalised hyperbolic family. Insur. Math. Econ. 86 (2019), pp. 98–114.
   Web of Science ®Google Scholar
• K. Ignatieva, and Z. Landsman, Estimating the tails of loss severity via conditional risk measures for the family of symmetric generalised hyperbolic distributions. Insur. Math. Econ. 65 (2015), pp. 172–186.
   Web of Science ®Google Scholar
• E. Jamshidi Eini, and H. Khaloozadeh, Tail variance for generalized skew-elliptical distribution. Com. Stat. Meth. (2020). doi:https://doi.org/10.1080/03610926.2020.1751853.
   Google Scholar
• P. Jorion, Risk2: measuring the risk in value at risk. Financ. Anal. J. 52 (1996), pp. 47–56.
   Google Scholar
• D. Kelker, Distribution theory of spherical distributions and location-scale parameter generalization. Sankh 32 (1970), pp. 831–869.
   Google Scholar
• J.H. Kim, Conditional tail moments of the exponential family and its related distributions. Nor. Amer. Act. J. 14 (2010), pp. 198–216.
   Google Scholar
• Z. Landsman, U. Makov, and T. Shushi, Extended generalized skew-elliptical distributions and their moments. Ind. J. Stat. 79 (2017), pp. 76–100.
   Google Scholar
• Z. Landsman, U. Makov, and T. Shushi, Tail conditional expectations for generalized skew-elliptical distributions. SSRN Elec. J. (2013), pp. 55–71. doi:https://doi.org/10.2139/ssrn.2298265
   Google Scholar
• Z. Landsman, U. Makov, and T. Shushi, Tail conditional moments for elliptical and log-elliptical distributions. Insur. Math. Econ. 71 (2016), pp. 179–188.
   Web of Science ®Google Scholar
• Z. Landsman, N. Pat, and J. Dhaene, Tail variance premiums for log-elliptical distributions. Insur. Math. Econ. 52 (2013), pp. 441–447.
   Web of Science ®Google Scholar
• Z. Landsman, and E.A. Valdez, Tail conditional expectations for elliptical distributions. Nor. Ame. Act. J 7 (2003), pp. 55–71.
   Google Scholar
• T.J. Linsmeier, and N.D. Pearson, Value at risk. Financ. Anal. J. 56 (2000), pp. 47–67.
   Google Scholar
• J.P. Morgan/Reuters, Risk Metrics Technical Document. 4nd ed, New York, Morgan Guaranty Trust Company, 1996.
   Google Scholar
• S. Nadarajah, and S. Kotz, Skewed distributions generated by the normal kernel. Stat. Prob. Let. 65 (2003), pp. 269–277.
   Web of Science ®Google Scholar
• N. Nematollahi, R. Farnoosh, and Z. Rahnamaei, Location-scale mixture of skew-elliptical distributions: looking at the robust modeling. Stat. Meth. 32 (2016), pp. 131–146.
   Google Scholar
• H. Panjer, Measurement of Risk, Solvency Requirements and Allocation of Capital Within Financial Conglomerates, Ontario, Canada, Res. Rep. Institute of Insurance and Pension Research, University of Waterloo, 2002, pp. 1–15.
   Google Scholar
• T. Shushi, Generalized skew-elliptical distributions are closed under affine transformations. Stat. Prob. Let. 134 (2018), pp. 1–4.
   Web of Science ®Google Scholar
• J. Tu, and G. Zhou, Data-generating process uncertainty: what difference does it make in portfolio decisions? J. Financ. Econ. 72 (2004), pp. 385–421.
   Web of Science ®Google Scholar
• R. Vernic, On the multivariate skew-normal distribution and its scale mixtures. An, St. Univ. Ovid. Const. 13 (2005), pp. 83–96.
   Google Scholar
• J. Wang, J. Boyer, and M.G. Genton, A skew-symmetric representation of multivariate distributions. Stat. Sini. 14 (2004), pp. 1259–1270.
   Web of Science ®Google Scholar