Tail asymptotics for dependent subexponential differences
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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.
Keywordssubexponential random variables differences dependence copulas mean excess function
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- 8.Boudreault M., Cossette H., Landriault D., and Marceau E., “On a risk model with dependence between interclaim arrivals and claim sizes,” Scand. Actuar. J., No. 5, 265–285 (2006).Google Scholar
- 9.Asimit A. V. and Badescu A. L., “Extremes on the discounted aggregate claims in a time dependent risk model,” Scand. Actuar. J., No. 2, 93–104 (2010).Google Scholar