Tail asymptotics for the sum of two heavy-tailed dependent risks

By Hansjörg Albrecher *, Søren Asmussen, Dominik Kortschak. 2006

86 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/50fcf55dfc1e491068fb5bc72325835b729f1a7a

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Citations in the corpus

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.”
Absolutely Continuous Copulas with Given Diagonal Sections (2008, background): “…given diagonal section (and, hence, tail dependence coefficients) have been largely considered in several financial applications: see, for example, Albrecher et al. (2006), Charpentier and Segers (2007), Frahm et al. (2005), Juri and Wüthrich (2002), Malevergne and Sornette (2006), Schmidt and…”
Tail behavior of sums and differences of log-normal random variables (2013, methodology): “6] for the denition of subexponentiality). Numerous publications were devoted to tail estimates for distributions of sums or more general functions of dependent sub-exponential random variables (see [2, 17, 19, 21, 22, 33] and 3 the references therein). Various bounds for tails of functions of gener”
Sums of Pairwise Quasi-Asymptotically Independent Random Variables with Consistent Variation (2009, methodology): “Pairwise Quasi-Asymptotically Variables 77 When considering the same problem, Albrecher et al.[1] and Kortschak and Albrecher[16] used copulas to model the dependence structure of the random variables.”
SUMS OF DEPENDENT NONNEGATIVE RANDOM VARIABLES WITH SUBEXPONENTIAL TAILS (2008, methodology): “x Pr(X2 > x|X1 = t) Pr(X2 > x) Pr(X2 > x)dF1(t) ≤ F1(x)F2(x) sup x<t<∞ Pr(X2 > x+ t− t|X1 = t) Pr(X2 > x+ t− t) = O(1)F1(x)F2(x).”
Tail Risk of Multivariate Regular Variation (2011, background): “The tail estimates of VaR of the sum are obtained in [2, 1, 4, 22, 13] in a similar spirit.”
Multivariate extremes and the aggregation of dependent risks: examples and counter-examples (2009, unknown): “following proposition; see for instance Davis and Resnick [9], Lemma 2.1 or Albrecher et al. [ 2 ], Corollary 3.2.”
Asymptotic Tail Probabilities of Sums of Dependent Subexponential Random Variables (2009, background): “[1], Tang [27], Kortschak and Albrecher [17], and Ko and Tang [16], among others.”
The Pareto Copula, Aggregation of Risks and the Emperor's Socks (2008, background): “An interesting case of the regular variation result given in the previous subsection was discussed from the copula point of view by Alink et al. (2004) and reviewed ib Albrecher et al. (2006).”