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. …

… Jan Dhaene and Marc Goovaerts acknowledge the support of the Fortis Chair on Financial
… Apparently, the cdf of Z has steps in 0 and in M. For the part in-between we could use a …

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, …

… Goovaerts risk measures. We will show that a mean value principle can be used to define the
Haezendonck–Goovaerts … –Goovaerts risk measure, called the generalized Haezendonck–…

… GOOVAERTS with m the number of coupled risks. For any i andy (1,7 = 1,2, ... n\ i^j) we
assume that Xj and X; are independent risks, except if they are members of the same couple (…

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 …

… The interested reader is referred to Goovaerts et al. (1984). The properties to be deemed …
(1999) and Shiu (2000)—and before that comprehensively in Goovaerts et al. (1984) and many …

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 …