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Tail approximations for sums of dependent regularly varying random variables under Archimedean copula models. (English) Zbl 1480.60140

Summary: 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.

MSC:

60G70 Extreme value theory; extremal stochastic processes
62H05 Characterization and structure theory for multivariate probability distributions; copulas
65C05 Monte Carlo methods
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