Modern Actuarial Risk Theory contains what every actuary needs to know about non-life
insurance mathematics. It starts with the standard material like utility theory, individual and …

The increasing complexity of insurance and reinsurance products has seen a growing
interest amongst actuaries in the modelling of dependent risks. For efficient risk management, …

In an insurance context, one is often interested in the distribution function of a sum of random
variables. Such a sum appears when considering the aggregate claims of an insurance …

In an insurance context, one is often interested in the distribution function of a sum of
random variables (rv’s). Such a sum appears when considering the aggregate claims of an …

In this paper we examine and summarize properties of several well-known risk measures that
can be used in the framework of setting solvency capital requirements for a risky business. …

The correlation order, which is defined as a partial order between bivariate distributions with
equal marginals, is shown to be a helpfull tool for deriving results concerning the riskiness …

In this contribution, the upper bounds for sums of dependent random variables X 1 +X 2 +⋯+X
n derived by using comonotonicity are sharpened for the case when there exists a random …

In the usual model of the collective risk theory, we are interested in the severity of ruin, as
well as its probability. As a quantitative measure, we propose G(u, y), the probability that for …

We consider the problem of determining appropriate solvency capital requirements for an
insurance company or a financial institution. We demonstrate that the subadditivity condition …

We develop a simple algorithm for the numerical calculation of finite-time ruin probabilities
in a general discrete-time risk process model. These probabilities can be used for the …