Stop-loss and limited loss random variables are two important transforms of a loss random variable and appear in many modelling problems in insurance, finance, and other fields. Risk levels of a loss variable and its transforms are often measured by risk measures. When only partial information...

In the field of the Design and Analysis of Computer Experiments (DACE) meta-models are used to approximate time-consuming simulations. These simulations often contain simulation-model errors in the output variables. In the construction of meta-models, these errors are often ignored....

Consider the set of probability measures on a product space with the property that all have the same marginal distributions on the coordinate spaces. This set may be viewed as a correspondence, when the marginal distributions are varied. Here, it is shown that this correspondence is continuous....

An improved version of a ruin probability formula due to Ignatov and Kaishev [Scand. Actu. J. 1 (2000) 46], allowing for the exact evaluation of the finite-time survival probability for discrete, dependent, individual claims, Poisson claim arrivals and arbitrary, increasing premium income...

This paper shows how de Finetti's book-making principle, commonly used to justify additive subjective probabilities, can be modified to agree with some nonexpected utility models. More precisely, a new foundation of the rank-dependent models is presented that is based on a comonotonic extension...

The aim of this paper is to develop some measure-theoretic methods for the study of large economic systems with individual-specific randomness and multiple optimal actions. In particular, for a suitably formulated continuum of correspondences, an exact version of the law of large numbers in...

By assuming that the underlying distribution belongs to the domain of attraction of an extreme value distribution, one can extrapolate the data to a far tail region so that a rare event can be predicted. However, when the distribution is in the domain of attraction of a Gumbel distribution, the...