Tail Approximations for Sums of Dependent Regularly Varying Random Variables Under Archimedean Copula Models

Hélène Cossette, Etienne Marceau (), Quang Huy Nguyen and Christian Y. Robert
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Hélène Cossette: Université Laval
Etienne Marceau: Université Laval
Quang Huy Nguyen: Université de Lyon, Université Lyon 1
Christian Y. Robert: Université de Lyon, Université Lyon 1

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 2, 461-490

Abstract: Abstract 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.

Keywords: Tail approximation; Archimedean copulas; Dependent regularly varying random variables; Conditional Monte Carlo simulation; Numerical bounds; 68U20; 65C05; 60G70 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-017-9614-z

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