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Some properties of the exponential distribution class with applications to risk theory
Cheng, Dongya,Ni, Fenglian,Pakes, Anthony G.,Wang, Yuebao 한국통계학회 2012 Journal of the Korean Statistical Society Vol.41 No.4
This paper derives some equivalent conditions for tail equivalence of a distribution G and the convolution G*H, where G belongs to the exponential distribution class and H is another distribution. This generalizes some existing sufficient conditions and gives further insight into closure properties of the exponential distribution class. If G also is O-subexponential, then the new conditions are satisfied. The obtained results are applied to investigating asymptotic behavior for the finite-time ruin probability in a discrete-time risk model with both insurance and financial risks, where the distributions of the insurance risk or the product of the two risks may not belong to the convolution equivalence distribution class.
Some properties of the exponential distribution class with applications to risk theory
Yuebao Wang,Dongya Cheng,Fenglian Ni,Anthony G. Pakes 한국통계학회 2012 Journal of the Korean Statistical Society Vol.41 No.4
This paper derives some equivalent conditions for tail equivalence of a distribution G and the convolution G∗H, where G belongs to the exponential distribution class andH is another distribution. This generalizes some existing sufficient conditions and gives further insight into closure properties of the exponential distribution class. If G also is O-subexponential,then the new conditions are satisfied. The obtained results are applied to investigating asymptotic behavior for the finite-time ruin probability in a discrete-time risk model with both insurance and financial risks, where the distributions of the insurance risk or the product of the two risks may not belong to the convolution equivalence distribution class.
Tail behavior of the sums of dependent and heavy-tailed random variables
Changjun Yu,Yuebao Wang,Dongya Cheng 한국통계학회 2015 Journal of the Korean Statistical Society Vol.44 No.1
In this paper, we investigate the tail asymptotic behavior of the partial sums, therandom sums and the weighted sums of heavy-tailed random variables (r.v.s.) undertwo new dependence structures, respectively. The increments are real-valued and havesubexponential∗ distributions, and the dependence structures can contain common linearlynegatively quadrant dependent r.v.s., some positively dependent r.v.s. and some otherr.v.s. The obtained results are used to derive the asymptotic estimation of the finite-timeruin probability for a nonstandard renewal risk model. In addition, some mutual relationsamong these two new dependence structures and some other relevant ones are discussed.