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Extremes

, Volume 21, Issue 4, pp 509–532 | Cite as

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

  • Zhaolei Cui
  • Edward Omey
  • Wenyuan Wang
  • Yuebao Wang
Article

Abstract

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.

Keywords

Semi-regular-variation tail Convolution Asymptotics Risk model Stochastic returns Ruin probability 

AMS 2000 Subject Classifications

Primary 60E07 60F99 

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Notes

Acknowledgements

The authors are grateful to two referees and Associate Editor for their valuable comments and suggestions which greatly improve the original version of the paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Zhaolei Cui
    • 1
  • Edward Omey
    • 2
  • Wenyuan Wang
    • 3
  • Yuebao Wang
    • 4
  1. 1.School of Mathematics and StatisticsChangshu Institute of TechnologySuzhouPeople’s Republic of China
  2. 2.Faculty of Economics and Business-Campus BrusselsKU LeuvenBrusselsBelgium
  3. 3.School of Mathematical SciencesXiamen UniversityXiamenPeople’s Republic of China
  4. 4.School of Mathematical SciencesSoochow UniversitySuzhouPeople’s Republic of China

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