Tail Distribution of the Maximum of Correlated Gaussian Random Variables

Zdravko Botev, Michel Mandjes and Ad Ridder
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Zdravko Botev: The University of New South Wales, Sydney, Australia
Michel Mandjes: University of Amsterdam, the Netherlands
Ad Ridder: VU University Amsterdam, the Netherlands

No 15-132/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: Rare event simulation; Correlated Gaussian; Tail probabilities; Sequential importance sampling (search for similar items in EconPapers)
JEL-codes: C61 C63 (search for similar items in EconPapers)
Date: 2015-12-15
New Economics Papers: this item is included in nep-ecm
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Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20150132

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