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Tail asymptotics for dependent subexponential differences

Albrecher, H. ; Asmussen, S. ; Kortschak, D.

In: Siberian Mathematical Journal, 2012, vol. 53, no. 6, p. 965-983

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    Titre
    • Tail asymptotics for dependent subexponential differences
    Auteur
    • Albrecher, H.. University of Lausanne, Lausanne, Switzerland
    • Asmussen, S.. Aarhus University, Aarhus, Denmark
    • Kortschak, D.. University of Lausanne, Lausanne, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Siberian Mathematical Journal, 2012, vol. 53, no. 6, p. 965-983. SP MAIK Nauka/Interperiodica
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:315587
    Summary
    We study the asymptotic behavior of ℙ(X − Y > 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 X − Y. Some explicit construction of the worst-case copula is provided in other cases