Insensitivity to Negative Dependence of the Asymptotic Behavior of Precise Large Deviations

By Qihe Tang. 2006

101 citations recorded by the source corpus.

Since the pioneering works of C.C. Heyde, A.V. Nagaev, and S.V. Nagaev in 1960's and 1970's, the precise asymptotic behavior of large-deviation probabilities of sums of heavy-tailed random variables has been extensively investigated by many people, but mostly it is assumed that the random variables under discussion are independent. In this paper, we extend the study to the case of negatively dependent random variables and we find out that the asymptotic behavior of precise large deviations is insensitive to the negative dependence.

Subfields: Finance, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/012c893d56fa4daff0d251feb70dd121f3633964

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In Finance

In Management Science and Operations Research

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Citations in the corpus

The Strong Law of Large Numbers for Extended Negatively Dependent Random Variables (2010, methodology): “1 of Ko and Tang (2008), in the following lemma we show a sufficient condition for the random variables Xk, k = 1,.”
Asymptotics for the ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims (2011, background): “[5], Tang [6, 7], Wang and Wang [8], Robert and Segers [9], Aleškevičienė et al.”
Tails of random sums of a heavy-tailed number of light-tailed terms (2007, background): “) = β−1x1−β. 2.3 Large deviations In order to analyse the tails of the compound sum S N, we need bounds on the probability of large deviations of S n. The ﬁrst bound is a special case of Lemma 2.3 in Tang (2006). Lemma 2.1 If E[Xr 1 ] < ∞ for some r > 1, then for each γ > 0 and q > 0, th”
Sums of Pairwise Quasi-Asymptotically Independent Random Variables with Consistent Variation (2009, background): “1 of Tang[27], the condition on the random variable in Theorem 3.”