In this paper we investigate the potential of Lévy copulas as a tool for modelling dependence between compound Poisson processes and their applications in insurance. We analyse characteristics regarding the dependence in frequency and dependence in severity allowed by various Lévy copula...

Stochastic loss reserving with dependence has received increased attention in the last decade. A number of parametric multivariate approaches have been developed to capture dependence between lines of business within an insurer's portfolio. Motivated by the richness of the Tweedie family of...

We consider the general class of spectrally positive Lévy risk processes, which are appropriate for businesses with continuous expenses and lump sum gains whose timing and sizes are stochastic. Motivated by the fact that dividends are paid periodically in real life, we study periodic dividend...

The paper is concerned with multiple claim arrays. We construct a broad and flexible family of models, where dependency is induced by common shock components. Models incorporate dependencies between observations both within arrays and between arrays. Arrays are of general shape (possibly with...

The Central Limit Theorem (CLT) is one of the most fundamental results in Statistics. It states that the standardized sample mean of a sequence of n mutually independent and identically distributed random variables with finite first and second moments converges in distribution to a standard...