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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Hélène Cossette & Etienne Marceau & Quang Huy Nguyen & Christian Y. Robert, 2019. "Tail Approximations for Sums of Dependent Regularly Varying Random Variables Under Archimedean Copula Models," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 461-490, June.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:2:d:10.1007_s11009-017-9614-z
    DOI: 10.1007/s11009-017-9614-z
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    References listed on IDEAS

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    Cited by:

    1. Chaoubi, Ihsan & Cossette, Hélène & Gadoury, Simon-Pierre & Marceau, Etienne, 2020. "On sums of two counter-monotonic risks," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 47-60.

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