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