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

Albrecher, Hansjörg; Asmussen, Søren; Kortschak, Dominik

doi:10.1007/s10687-006-0011-1

Cited by 64 publications

(47 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…7. Similar limit results are found in Lemma 2.7 of Albrecher et al (2006) and Theorem 2.1 of Ko and Tang (2008). They assumed that one of the marginal distributions of the two asymptotically independent variables X and Y , say the distribution of X, is subexponential (i.e.…”

Section: Assumptions Suppose That (X Y ) Is a Pair Of Random Variabmentioning

confidence: 59%

“…• Very different tail behavior is exhibited in Theorem 2.10 of Albrecher et al (2006), in which a joint distribution of (X, Y ) was given making X and Y asymptotically independent with identical marginal distribution F ∈ MDA( ), but…”

Section: Introductionmentioning

confidence: 98%

“…Recent results can be found in Albrecher et al (2006), Klüppelberg and Resnick (2008), Wang and Tang (2006), Asmussen and Rojas-Nandayapa (2008), Alink et al (2004), Embrechts and Puccetti (2006), and Ko and Tang (2008). Approximating this probability helps us evaluate risk measures for investment portfolios as well as estimating credit risk.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Aggregation of rapidly varying risks and asymptotic independence

Mitra¹,

Resnick²

2009

Adv. Appl. Probab.

View full text Add to dashboard Cite

We study the tail behavior of the distribution of the sum of asymptotically independent risks whose marginal distributions belong to the maximal domain of attraction of the Gumbel distribution. We impose conditions on the distribution of the risks (X, Y ) such that P(X +Y > x) ∼ (constant) P(X > x). With the further assumption of nonnegativity of the risks, the result is extended to more than two risks. We note a sufficient condition for a distribution to belong to both the maximal domain of attraction of the Gumbel distribution and the subexponential class. We provide examples of distributions which satisfy our assumptions. The examples include cases where the marginal distributions of X and Y are subexponential and also cases where they are not. In addition, the asymptotic behavior of linear combinations of such risks with positive coefficients is explored, leading to an approximate solution of an optimization problem which is applied to portfolio design.

show abstract

Section: Assumptions Suppose That (X Y ) Is a Pair Of Random Variabmentioning

confidence: 59%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Aggregation of rapidly varying risks and asymptotic independence

Mitra¹,

Resnick²

2009

Adv. Appl. Probab.

View full text Add to dashboard Cite

show abstract

“…There has been a particular interest in understanding the tail behavior of the sum of asymptotically independent random variables with heavy tails (see Albrecher et al, 2006, Ko and Tang, 2008, Asmussen and Rojas-Nandayapa, 2008, Geluk and Tang, 2009, and Mitra and Resnick, 2009 3.1. Fréchet case.…”

Section: Main Results Under Asymptotic Independencementioning

confidence: 99%

Asymptotics for risk capital allocations based on Conditional Tail Expectation

Asimit

Furman

Tang

et al. 2011

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

Abstract. 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-atRisk (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.

show abstract

“…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). Suppose that d = 2 and that X = (X (1) , X (2) ), where F (2) .…”

Section: An Interesting Special Casementioning

confidence: 99%

The Pareto Copula, Aggregation of Risks, and the Emperor's Socks

Klüppelberg

Resnick

2008

J. Appl. Probab.

View full text Add to dashboard Cite

The copula of a multivariate distribution is the distribution transformed so that onedimensional marginal distributions are uniform. We review a different transformation of a multivariate distribution which yields standard Pareto for the marginal distributions, and we call the resulting distribution the Pareto copula. Use of the Pareto copula has a certain claim to naturalness when considering asymptotic limit distributions for sums, maxima, and empirical processes. We discuss implications for aggregation of risk and offer some examples.

show abstract

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

Cited by 64 publications

References 31 publications

Aggregation of rapidly varying risks and asymptotic independence

Aggregation of rapidly varying risks and asymptotic independence

Asymptotics for risk capital allocations based on Conditional Tail Expectation

The Pareto Copula, Aggregation of Risks, and the Emperor's Socks

Contact Info

Product

Resources

About