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Tail Asymptotics for the Sum of two Heavy-tailed Dependent Risks

by Hansjörg Albrecher and Søren Asmussen
Thiele Research Reports Number 9 (August 2005)
Let $X_1,X_2$ denote positive exchangable heavy-tailed random variables with continuous marginal distribution function $F$. The asymptotic behavior of the tail of $X_1+X_2$ is studied in a general copula framework and some bounds and extremal properties are provided. For more specific assumptions on $F$ and the underlying dependence structure of $X_1$ and $X_2$, we survey explicit asymptotic results available in the literature and add several new cases.
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This publication also serves as Research Reports number 462