In 1983 Cox and Kemperman proved that Ef(ξ)+Ef(η)≤Ef(ξ+η) for functions f with convex second derivative and independent centered random variables ξ and η. We suggest another proof, show that the minimal moment restrictions are sufficient, and write out a less restrictive condition on f...

Foster and Hart proposed an operational measure of riskiness for discrete random variables. We show that their defining equation has no solution for many common continuous distributions including many uniform distributions, e.g. We show how to extend consistently the definition of riskiness to...

In this paper we apply the idea of the WKB method to derive an effective single lognormal approximation for the probability distribution of the sum of two correlated lognormal variables. An approximate probability distribution of the sum is determined in closed form, and illustrative numerical...

In the context of representation theorems for conditional and multi-period risk measures, we will extend the work, started in [9], on locally convex modules over the ring $\lambda= L^\infty(G)$, by adding an order or a lattice structure. The dual spaces of lattice -modules turn out to be...

We show that the logarithms of gamma random variables are α-selfdecomposable, and apply the result to show that logarithms of several positive random variables are 1-selfdecomposable.