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Siberian Mathematical Journal

, Volume 53, Issue 6, pp 965–983 | Cite as

Tail asymptotics for dependent subexponential differences

  • H. Albrecher
  • S. Asmussen
  • D. KortschakEmail author
Article

Abstract

We study the asymptotic behavior of ℙ(XY > u) as u → ∞, where X is subexponential, Y is positive, and the random variables X and Y may be dependent. We give criteria under which the subtraction of Y does not change the tail behavior of X. It is also studied under which conditions the comonotonic copula represents the worst-case scenario for the asymptotic behavior in the sense of minimizing the tail of XY. Some explicit construction of the worst-case copula is provided in other cases.

Keywords

subexponential random variables differences dependence copulas mean excess function 

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.University of LausanneLausanneSwitzerland
  2. 2.Aarhus UniversityAarhusDenmark
  3. 3.University of LyonLyonFrance

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