Sums of Dependent Nonnegative Random Variables with Subexponential Tails

Ko, Bangwon; Tang, Qihe

doi:10.1017/s0021900200003971

Cited by 22 publications

(25 citation statements)

References 11 publications

(8 reference statements)

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: 58%

“…random variables X and Y belong to the class MDA( )∩S, an issue is the relative strength of our conditions versus those of Theorem 2.1 of Ko and Tang (2008). We cannot show that either set of conditions implies the other.…”

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

confidence: 85%

“…It is well known that the lognormal distribution belongs to the class MDA( ) ∩ S. In Example 3.5, below, we show that (X, Y ) satisfies our set of conditions. Here we show that this example does not satisfy Assumption 2.1 of Ko and Tang (2008), i.e. for all x * > 0,…”

mentioning

confidence: 85%

“…We cannot show that either set of conditions implies the other. Below we present an example which satisfies our set of conditions, but does not satisfy the set of conditions given in Theorem 2.1 of Ko and Tang (2008). Thus, our set of conditions is not stronger.…”

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

confidence: 96%

“…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 4 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: 58%

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

confidence: 85%

mentioning

confidence: 85%

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

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Aggregation of rapidly varying risks and asymptotic independence

Mitra¹,

Resnick²

2009

Adv. Appl. Probab.

View full text Add to dashboard Cite

show abstract

Asymptotic Tail Probabilities of Sums of Dependent Subexponential Random Variables

Geluk¹,

Tang

2008

J Theor Probab

Self Cite

104

View full text Add to dashboard Cite

In this paper we study the asymptotic behavior of the tail probabilities of sums of dependent and real-valued random variables whose distributions are assumed to be subexponential and not necessarily of dominated variation. We propose two general dependence assumptions under which the asymptotic behavior of the tail probabilities of the sums is the same as that in the independent case. In particular, the two dependence assumptions are satisfied by multivariate Farlie-Gumbel-Morgenstern distributions.

show abstract