It is shown that for elliptically distributed bivariate random vectors, the riskiness and dependence strength of random portfolios, in the sense of the univariate convex and bivariate concordance stochastic orders respectively, can be simply characterised in terms of the vector's...

We study a multivariate extension of the univariate exponential dispersion Tweedie family of distributions. The class, referred to as the multi-variate Tweedie family (MTwF), on the one hand includes multivariate Poisson, gamma, inverse Gaussian, stable and compound Poisson distributions and on...

Rogers & Shi (1995) have used the technique of conditional expectations to derive approximations for the distribution of a sum of lognormals. In this paper we extend their results to more general sums of random variables. In particular we study sums of functions of dependent random variables...

Actuaries are often faced with the task of estimating tails of loss distributions from just a few observations. Thus estimates of tail probabilities (reinsurance prices) and percentiles (solvency capital requirements) are typically subject to substantial parameter uncertainty. We study the bias...

This paper introduces a multivariate tail covariance (MTCov) measure, which is a matrix-valued risk measure designed to explore the tail dispersion of multivariate loss distributions. The MTCov is the second multivariate tail conditional moment around the MTCE, the multivariate tail conditional...