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In this paper, we compare two numerical methods for approximating theprobability that the sum of dependent regularly varying random variablesexceeds a high threshold under Archimedean copula models. The first method isbased on conditional Monte Carlo. We present four estimators and show that mostof them have bounded relative errors. The second method is based on analyticalexpressions of the multivariate survival or cumulative distribution functionsof the regularly varying random variables and provides sharp and deterministicbounds of the probability of exceedance. We discuss implementation issues andillustrate the accuracy of both procedures through numerical studies.

Tail approximations for sums of dependent regularly varying random variables under Archimedean copula models