Rogers and 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...

Brown et al. (2006) derive a Stein-type inequality for the multivariate Student’s t-distribution. We generalize their result to the family of (multivariate) generalized hyperbolic distributions and derive a lower bound for the variance of a function of a random variable.

Brown et al. (2006) derive a Stein-type inequality for the multivariate Student-t distribution. We generalize their result to the family of (multivariate) generalized hyperbolic distributions and derive a lower bound for the variance of a function of a random variable

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...

When two random variables are bivariate normally distributed Stein's original lemma allows to conveniently express the covariance of the first variable with a function of the second. Landsman & Neslehova (2007) extend this seminal result to the family of multivariate elliptical distributions. In...

In this paper we derive expressions for the Tail Variance and the Tail Variance Premium of risks in a multivariate log-elliptical setting. The theoretical results are illustrated by considering lognormal and log-Laplace distributions. We also derive approximate expressions for a Tail...