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Tail Distribution of the Maximum of Correlated Gaussian Random Variables

Author

Listed:
  • Zdravko Botev

    (The University of New South Wales, Sydney, Australia)

  • Michel Mandjes

    (University of Amsterdam, the Netherlands)

  • Ad Ridder

    (VU University Amsterdam, the Netherlands)

Abstract

In this article we consider the efficient estimation of the tail distribution of the maximum of correlated normal random variables. We show that the currently recommended Monte Carlo estimator has difficulties in quantifying its precision, because its sample variance estimator is an inefficient estimator of the true variance. We propose a simple remedy: to still use this estimator, but to rely on an alternative quantification of its precision. In addition to this we also consider a completely new sequential importance sampling estimator of the desired tail probability. Numerical experiments suggest that the sequential importance sampling estimator can be significantly more efficient than its competitor.

Suggested Citation

  • Zdravko Botev & Michel Mandjes & Ad Ridder, 2015. "Tail Distribution of the Maximum of Correlated Gaussian Random Variables," Tinbergen Institute Discussion Papers 15-132/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20150132
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    References listed on IDEAS

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    1. Enkelejd Hashorva & Jürg Hüsler, 2003. "On multivariate Gaussian tails," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 507-522, September.
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    More about this item

    Keywords

    Rare event simulation; Correlated Gaussian; Tail probabilities; Sequential importance sampling;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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