In actuarial research, distortion-, mean value- and Haezendonck-Goovaerts risk measures are concepts that are usually treated separately. In this paper we indicate and characterize the relation between the different risk measures, as well as their relation to convex risk measures. While it is...

In the traditional approach to life contingencies only decrements are assumed to be stochastic. In this contribution we consider the distribution of a life annuity (and a portfolio of life annuities) when also the stochastic nature of interest rates is taken into account. Although the literature...

In a recent paper, Salminen and Yor (2004b) relate the distribution of the Dufresne's reflected perpetuity to the hitting time of a reflected Bessel process. In this contribution, we adapt the results of Salminen and Yor (2004b) in several ways. First, we use spectral theory to obtain a series...

In this paper we give some methods to set up confidence bounds for the discounted IBNR reserve. We start with a loglinear regression model and estimate the parameters by maximum likelihood such as given for example in Doray, 1996. The knowledge of the distribution function of the discounted IBNR...

We examine properties of risk measures that can be considered to be in line with some quot;best practicequot; rules in insurance, based on solvency margins. We give ample motivation that all economic aspects related to an insurance portfolio should be considered in the definition of a risk...

In their seminal paper, Gerber and Shiu (1994) introduced the concept of the Esscher transform for option pricing. As examples they considered the shifted Poisson process, the random walk, a shifted gamma process and a shifted inverse Gaussian process to describe the logarithm of the stock...