Asymptotics of convolution with the semi-regular-variation tail and its application to risk

In this paper, according to a certain criterion, we divide the exponential distribution class into some subclasses. One of them is closely related to the regular-variation-tailed distribution class, and is called the semi-regular-variation-tailed distribution class. The new class possesses several n...

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Bibliographic Details
Published in:Extremes (Boston) 2018-12, Vol.21 (4), p.509-532
Main Authors: Cui, Zhaolei, Omey, Edward, Wang, Wenyuan, Wang, Yuebao
Format: Article
Language:English
Subjects:
Asymptotic properties
Civil Engineering
Convolution
Economics
Environmental Management
Finance
Hydrogeology
Insurance
Management
Mathematics and Statistics
Probability distribution functions
Quality Control
Random variables
Reliability
Safety and Risk
Statistics
Statistics for Business
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Summary:In this paper, according to a certain criterion, we divide the exponential distribution class into some subclasses. One of them is closely related to the regular-variation-tailed distribution class, and is called the semi-regular-variation-tailed distribution class. The new class possesses several nice properties, although distributions in it are not convolution equivalent. We give the precise tail asymptotic expression of convolutions of these distributions, and prove that the class is closed under convolution. In addition, we do not need to require the corresponding random variables to be identically distributed. Finally, we apply these results to a discrete time risk model with stochastic returns, and obtain the precise asymptotic estimation of the finite time ruin probability.
ISSN:1386-1999
1572-915X
DOI:10.1007/s10687-018-0326-8