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...

Teicher [1955] proved that the probability a Poisson distribution with mean k takes on a value of k or less is monotonically decreasing in k. I extend this inequality by proving that the probability a Poisson distribution with mean zk takes on a value of k or less is monotonically decreasing for...

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...

We consider usual stochastic and likelihood ratio orders. It has already been proven that the comparison of two random vectors (or variables) in the sense of likelihood ratio implies their comparison in the sense of usual stochastic order. In this paper, we will prove that the reverse is also...

This paper studies the approximation of extreme quantiles of random sums of heavy-tailed random variables, or more specifically, subexponential random variables. A key application of this approximation is the calculation of operational VaR (value at risk) for financial institutions, to determine...

In this paper, we discuss a generalization of the collective risk model and of Panjer's recursion. The model we consider consists of several business lines with dependent claim numbers. The distributions of the claim numbers are assumed to be Poisson mixture distributions. We let the claim...

For evaluating the probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distribution whose probabilities can be dealt with based...