In this article, we investigate the tail probability of the product of finitely many non-negative dependent random variables. They follow distributions from max-domains of attraction of extreme value distributions and their dependence is modeled via a multivariate Farlie–Gumbel–Morgenstern...

When correlations between assets turn positive, multi-asset portfolios can become riskier than single assets. This article presents the estimation of tail risk at very high quantiles using a semiparametric estimator which is particularly suitable for portfolios with a large number of assets. The...

This paper deals with the asymptotic behavior for the tail probability of randomly weighted sums of subexponential random variables under a dependence structure, where the random weights and the corresponding summands are dependent.

Let [X] and {X} be the integer and the fractional parts of a random variable X. The conditional distribution function Fn(x)=P({X}≤x|[X]=n) for an integer n is investigated. Fn for a large n is regarded as the distribution of a roundoff error in an extremal event. For most well-known continuous...

In this paper we investigate asymptotic behavior of the tail probability for subordinated self-similar processes with regularly varying tail probability. We show that the tail probability of the one-dimensional distributions and the supremum tail probability are regularly varying with the...

In this paper we estimate tail probabilities for the sum of Lognormal distributions. We propose to use a defensive mixture, and develop a method of finding the optimal density via the EM algorithm; we also consider the technique which assumes the importance sampling density to belong to the same...

Let {Xi, i[greater-or-equal, slanted]1} be a sequence of i.i.d. random vectors inRd, and let[nu]p, 0p1, be a positive, integer valued random variable, independent ofXis. The[nu]-stable distributions are the weak limits of properly normalized random sums [summation...