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Languages: English
Types: Article
Subjects: HG
An investigation of the limiting behavior of a risk capital allocation rule based on the Conditional Tail Expectation (CTE) risk measure is carried out. More specifically, with the help of general notions of Extreme Value Theory (EVT), the aforementioned risk capital allocation is shown to be asymptotically proportional to the corresponding Value-at-Risk (VaR) risk measure. The existing methodology acquired for VaR can therefore be applied to a somewhat less well-studied CTE. In the context of interest, the EVT approach is seemingly well-motivated by modern regulations, which openly strive for the excessive prudence in determining risk capitals.
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    • Albrecher, H., Asmussen, S. and Kortschak, D. and 2006. “Tail asymptotics for the sum of two heavy-tailed dependent risks,” Extremes 9(2), 107 - 130.
    • Alink, S., Lo¨we, M. and Wu¨thrich, M.V. 2005. “Analysis of the expected shortfall of aggregate dependent risks,” ASTIN Bulletin, 35(1), 25 - 43.
    • Asimit, A. V. and Badescu, A. L. 2010. “Extremes on the discounted aggregate claims in a time dependent risk model,” Scandinavian Actuarial Journal, 2, 93-104.
    • Asimit, A.V. and Jones, B.L. 2008. “Asymptotic tail probabilities for large claims reinsurance of a portfolio of dependent risks,” ASTIN Bulletin, 38(1), 147 - 159.
    • Asmussen, S. and Rojas-Nandayapa, L. 2008. “Asymptotics of sums of lognormal random variables with Gaussian copula ,” Statistics and Probability Letters, 78(16), 2709 - 2714.
    • Balkema, A.A. and de Haan, L. 1974. “Residual life time at great age,” The Annals of Probability, 2(5), 792 - 804.
    • Bu¨hlmann, H. 1980. “An economic premium principle,” ASTIN Bulletin, 11(1), 52 - 60.
    • Cai, J. and Li., H. 2005. “Conditional tail expectations for multivariate phase-type distributions,” Journal of Applied Probability, 42(3), 810 - 825.
    • Cai, J. and Tang, Q. 2004. “On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications,” Journal of Applied Probability, 41(1), 117 - 130.
    • Charpentier, A. and Segers, J. 2009. “Tails of multivariate Archimedean copulas,” Journal of Multivariate Analysis, 100(7), 1521 - 1537.
    • Chiragiev, A. and Landsman, Z. 2007. “Multivariate Pareto portfolios: TCE-based capital allocation and divided differences,” Scandinavian Actuarial Journal, 2007(4), 261 - 280.
    • Davis, R.A. and Resnick, S.I. 1996. “Limit theory for bilinear processes with heavy-tailed noise,” The Annals of Applied Probability, 6(4), 1191 - 1210.
    • Dhaene, J., Denuit, M. and Vanduffel, S. 2009. “Correlation order, merging and diversification,” Insurance: Mathematics and Economics, 45(3), 325 - 332.
    • 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(2), 855 - 863.
    • Dhaene, J., Tsanakas, A., Valdez, E. and Vanduffel, E. 2011. “Optimal capital allocation principles, ” Journal of Risk and Insurance, 78.
    • Dhaene, J., Vanduffel, S., Goovaerts, M.J., Kaas, R., Tang, Q. and Vyncke, D. 2006. “Risk measures and comonotonicity: a review,” Stochastic Models, 22, 573 - 606.
    • Embrechts, P., Klu¨ppelberg, C. and Mikosch, T. 1997. Modeling Extremal Events for Insurance and Finance. Springer-Verlag, Berlin.
    • Fisher, R.A. and Tippett, L.H.C. 1928. “Limiting forms of the frequency distribution of the largest or smallest member of a sample,” Mathematical Proceedings of the Cambridge Philosophical Society, 24(2), 180 - 190.
    • Furman, E. and Landsman, Z. 2005. “Risk capital decomposition for a multivariate dependent gamma portfolio,” Insurance: Mathematics and Economics, 37(3), 635 - 649.
    • Furman, E. and Landsman, Z. 2006. “Tail variance premium with applications for elliptical portfolio of risks,” ASTIN Bulletin, 36(2), 433 - 462.
    • Furman, E. and Landsman, Z. 2008. “Economic capital allocations for non-negative portfolios of dependent risks,” ASTIN Bulletin, 38(2), 601 - 619.
    • Furman, E. and Zitikis, R. 2008a. “Weighted premium calculation principles,” Insurance: Mathematics and Economics, 42(1), 459 - 465.
    • Furman, E. and Zitikis, R. 2008b. “Weighted risk capital allocations,” Insurance: Mathematics and Economics, 43(2), 263 - 269.
    • Geluk, J. and Tang, Q. 2009. “Asymptotic tail probabilities of sums of dependent subexponential random variables,” Journal of Theoretical Probability, 22(4), 871 - 882.
    • Genest, C., Ghoudi, K. and Rivest, L.P. 1998. “Discussions of understanding relationships using copulas,” North American Actuarial Journal, 2(3), 143 - 149.
    • Gnedenko, B.V. 1943. “Sur la distribution limit´e du terme maximum d'une s´erie al´eatoaire,” Annals of Mathematics, 44, 423 - 453.
    • Goldie, C.M. and Resnick, S. 1988. “Distributions that are both subexponential and in the domain of attraction of an extreme-value distribution,” Advances in Applied Probability 20(4), 706 - 718.
    • Hashorva, E., Pakes, A.G. and Tang, Q. 2010. “Asymptotics of random contractions,” Insurance: Mathematics and Economics, 47(3), 405 - 414.
    • Joe, H. and Li, L. 2011. “Tail risk of multivariate regular variation,” Methodology and Computing in Applied Probability, to appear.
    • Juri, A. and Wu¨thrich, M. V., 2003. “Tail dependence from a distributional point of view, ” Extremes, 6(3), 213-246.
    • Kallenberg, O. 1983. Random Measures, 3rd edition Akademie-Verlag, Berlin.
    • Khoudraji, A. 1995. “Contributions `a l'´etude des copules et `a la mod´elasion des valeurs extrˆemes bivari´ees,” Ph.D. thesis, Universit´e Laval, Qu´ebec, Canada.
    • Klu¨ppelberg, C. and Resnick, S.I. 2008. “The pareto copula, aggregation of risks, and the emperor's socks,” Journal of Applied Probability, 45(1), 67 - 84.
    • Ko, B. and Tang, Q. 2008. “Sums of dependent nonnegative random variables with subexponential tails,” Journal of Applied Probability, 45(1), 85-94.
    • Kortschak, D. and Albrecher, H. 2009. “Asymptotic results for the sum of dependent nonidentically distributed random variables,” Methodology and Computing in Applied Probability 11(3), 279 - 306.
    • Landsman, Z. and Valdez, E. 2003. “Tail conditional expectation for elliptical distributions,” North American Actuarial Journal, 7(4), 55 - 71.
    • Li, J., Tang, Q. and Wu, R. 2010. “Subexponential tails of discounted aggregate claims in a time- dependent renewal risk model,” Advances in Applied Probability 42(4), 1126 - 1146.
    • McNeil, A.J., Frey, R. and Embrechts, P. 2005. Quantitative Risk Management. Princeton University Press, Princeton, NJ.
    • Mitra, A. and Resnick, S.I. 2009. “Aggregation of rapidly varying risks and asymptotic independence,” Advances in Applied Probability, 41(3), 797 - 828.
    • Nelsen, R. B. 1999. An Introduction to Copulas. Springer-Verlag, New York.
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