We consider the problem of representing claims for coherent risk measures. For this purpose we introduce the concept of (weak and strong) time-consistency with respect to a portfolio of assets, generalizing the one defined in Delbaen [7]. In a similar way we extend the notion of m-stability, by introducing weak and strong versions. We then prove that the two concepts of mstability and time-cons...

Known vulnerabilities which have been discovered but not patched represents a security risk which can lead to considerable financial damage or loss of reputation. They include vulnerabilities that have either no patches available or for which patches are applied after some delay. Exploitation is even possible before public disclosure of a vulnerability. This paper formally defines risk measures...

Two main axiomatically based risk measures are the coherent risk measure, which assumes subadditivity for random variables, and the insurance risk measure, which assumes additivity for comonotonic random variables. We propose a new, data based, risk measure, called natural risk statistic, that is characterized by a new set of axioms. The new axioms only require subadditivity for comonotonic ran...

In this paper, we present a new security risk assessment method of website based on generalized fuzzy numbers. First, we present a new similarity measure between generalized fuzzy numbers. We also prove some properties of the proposed similarity measure and make an experiment to use 18 sets of generalized fuzzy numbers to compare the experimental results of the proposed method with the existing...

We use data extracted from many weblogs to identify the underlying relations of a set of companies in the Standard and Poor (S&P) 500 index. We define a pairwise similarity measure for the companies based on the weblog articles and then apply a graph clustering procedure. We show that it is possible to capture some interesting relations between companies using this method. As an application of ...

Let (Ω,Σ) be a measurable space and let B(Σ) denote the Banach space of bounded, Σ-measurable functions on Ω equipped with the sup-norm. Ω is the set of states of nature and B(Σ) is the set of all (measurable) risks (see Artzner et al. [2]). A measure of risk is a mapping ρ : B(Σ) −→ R. Coherent risk measures were introduced in [5] (under the name of "upper expectations") and further studied in...

Dhaene, Denuit, Goovaerts, Kaas & Vyncke (2002a,b) have studied convex bounds for a sum of dependent random variables and applied these to sums of log-normal random variables. In particular, they have shown how these convex bounds can be used to derive closed-form approximations for several of the risk measures of such a sum. In this paper we investigate to which extent their general results on...

+ e − collisions: a complete 1-loop calculation. Abstract We present the first complete 1-loop diagrammatic calculation of the cross sections for the neutral Higgs production processes e + e − → Z 0 h 0 and e + e − → A 0 h 0 in the minimal supersymmetric standard model. We compare the results from the diagrammatic calculation with the corresponding ones of the simpler and compact effective pote...