Precise large deviations for widely orthant dependent random variables with dominatedly varying tails

Wang, Kaiyong; Yang, Yang; Lin, Jin-Guan

doi:10.1007/s11464-012-0227-0

Cited by 24 publications

(17 citation statements)

References 23 publications

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“…For more details and applications of the class D, the readers are referred to Li, Wang, andWang (2009), Shneer (2004), Wang and Yang (2005), Zhou, Wang, and Wang (in press …”

Section: X) B(x) and B(x) A(x) And A(x) B(x) If A(x) = O(1)b(x) And mentioning

confidence: 99%

Randomly weighted sums with dominated varying-tailed increments and application to risk theory

Gao

Wang

2010

Journal of the Korean Statistical Society

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a b s t r a c tThis paper achieves some weakly asymptotic formulas of the tail probability of randomly weighted sums n i=1 Θ i X i and their maxima, where {X i , i ≥ 1} are bivariate upper tail independent random variables with common distribution F belonging to the dominant variation class, and {Θ i , i ≥ 1} are other nonnegative random variables and independent of {X i , i ≥ 1}. Particularly, when F belongs to the consistent variation class, some asymptotic formulas are established. An application to risk theory is proposed. The obtained results extend and improve the existing results of Zhang, Shen, and Weng (2009).

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“…For more details and applications of the class D, the readers are referred to Li, Wang, andWang (2009), Shneer (2004), Wang and Yang (2005), Zhou, Wang, and Wang (in press …”

Section: X) B(x) and B(x) A(x) And A(x) B(x) If A(x) = O(1)b(x) And mentioning

confidence: 99%

Randomly weighted sums with dominated varying-tailed increments and application to risk theory

Gao

Wang

2010

Journal of the Korean Statistical Society

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“…Furthermore, we will use the following assumption, which was given by Yang and Wang [31] when they investigated the precise large deviations for extendedly negatively dependent random variables. Wang et al [30] also used this assumption when they studied the precise large deviations for widely orthant dependent random variables. Assumption 1.5 For all i ≥ 1, F i ∈ D .…”

Section: Assumption 13 There Exists a Distribution F Such That The Dmentioning

confidence: 99%

Precise large deviations for the aggregate claims in a dependent compound renewal risk model

Wang

Chen

2019

J Inequal Appl

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We consider a dependent compound renewal risk model, where the interarrival times of accidents and the claim numbers follow a dependence structure characterized by a conditional tail probability and the claim sizes have a pairwise negatively quadrant dependence structure or a related dependence structure with the upper tail asymptotical dependence structure. When the distributions of the claim sizes belong to the dominated variation distribution class, we give the asymptotic lower and upper bounds for the precise large deviations of the aggregate claims.

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“…Chen et al [9] extended the previous results of Liu [11] to random sums with consistently varying tails. Wang et al [10] considered a wider dependent structure and investigated the precise large deviations for the partial sums with dominatedly varying tails.…”

Section: Isrn Applied Mathematicsmentioning

confidence: 99%

“…Some earlier work, for the case { , ≥ 1} are independent, we refer the reader to see Cline and Hsing [1], Klüppelberg and Mikosch [2], Tang et al [3], Ng et al [4], Konstantinides and Loukissas [5] and Loukissas [6], and so forth; for the case { , ≥ 1} are negatively dependent, see Chen and Zhang [7], Tang [8], Konstantinides and Loukissas [5], Chen et al [9] and Wang et al [10], and so forth.…”

Section: Introductionmentioning

confidence: 99%

Precise Large Deviations for Random Sums of END Random Variables with Dominated Variation

Chen

2013

ISRN Applied Mathematics

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We investigate the precise large deviations for random sums of extended negatively dependent random variables with long and dominatedly varying tails. We find out that the asymptotic behavior of precise large deviations of random sums is insensitive to the extended negative dependence. We apply the results to a generalized dependent compound renewal risk model including premium process and claim process and obtain the asymptotic behavior of the tail probabilities of the claim surplus process.

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Precise large deviations for widely orthant dependent random variables with dominatedly varying tails

Cited by 24 publications

References 23 publications

Randomly weighted sums with dominated varying-tailed increments and application to risk theory

Randomly weighted sums with dominated varying-tailed increments and application to risk theory

Precise large deviations for the aggregate claims in a dependent compound renewal risk model

Precise Large Deviations for Random Sums of END Random Variables with Dominated Variation

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