Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness

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Multivariate extremes and the aggregation of dependent risks: examples and counter-examples (2009, unknown): “Several authors mention the substantial influence of the transition from a finite to an infinite mean model on the additivity properties of VaR; see for instance Nešlehová et al. (2006), Embrechts et al. (2008), Ibragimov and Walden (2007) and Jang and Jho (2007).”
Tail Risk of Multivariate Regular Variation (2011, background): “The tail estimates of VaR of the sum are obtained in Alink et al. (2004, 2007), Albrecher et al. (2006), Kortschak and Albrecher (2009), Embrechts et al. (2009) in a similar spirit.”
Asymptotic Analysis of Multivariate Tail Conditional Expectations (2012, result): “Note that the tail estimates for VaRp( ∑d i=1Xi) in terms of the marginal VaR are discussed in [2, 1, 4, 9], and our tail estimate for TCE in terms of VaR complements these asymptotic results.”