One way to formulate a multivariate probability distribution with dependent univariate margins distributed gamma is by using the closure under convolutions property. This direction yields an additive background risk model, and it has been very well-studied. An alternative way to accomplish the...

A prominent problem in actuarial science is to define, or describe, premium calculation principles (pcp's) that satisfy certain properties. A frequently used resolution of the problem is achieved via distorting (e.g., lifting) the decumulative distribution function, and then calculating the...

By extending the notion of weighted premium calculation principles, we introduce weighted risk capital allocations, explore their properties, and develop computational methods. When achieving these goals, we find it particularly fruitful to relate the weighted allocations to general Stein-type...

We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with the new paradigm of prudent risk management. This...

Convenient expressions for the Esscher pricing functional in the context of the compound Poisson processes with dependent loss amounts and loss inter-arrival times are developed. To this end, the moment generating function of the aforementioned dependent processes is derived and studied. Various...

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

A multivariate distribution possessing arbitrarily parameterized Pareto margins is formulated and studied. The distribution is believed to allow for an adequate modeling of dependent heavy tailed risks with a non-zero probability of simultaneous loss. Numerous links to certain existing...

An investigation of the limiting behavior of a risk capital allocation rule based on the Conditional Tail Expectation (CTE) risk measure is carried out. More specifically, with the help of general notions of Extreme Value Theory (EVT), the aforementioned risk capital allocation is shown to be...