Distributional Transforms, Probability Distortions, and Their Applications

In this paper we provide a general mathematical framework for distributional transforms, which allows for many examples that are used extensively in the literature of finance, economics, and optimization. We put a special focus on the class of probability distortions, which is a fundamental tool in decision theory. As our main results, we characterize distributional transforms satisfying various properties, and this includes an equivalent set of conditions which forces a distributional transform to be a probability distortion. As the first application, we construct new risk measures using distributional transforms. Sufficient and necessary conditions are given to ensure the convexity or coherence of the generated risk measures. In the second application, we introduce a new method for sensitivity analysis of risk measures based on composition groups of probability distortions. Finally, we construct probability distortions describing a change of measures with an example in option pricing.

Analysis and implementation of the impact of change: application to heterogeneity algorithms in enterprise architecture

<p><span lang="EN-US">Measurements play an important role in many scientific fields in general and in</span><span lang="EN-US">the</span><span lang="EN-US">analysis</span><span lang="EN-US">of</span><span lang="EN-US">enterprise</span><span lang="EN-US">architecture</span><span lang="EN-US">in</span><span lang="EN-US">particular.</span><span lang="EN-US">In software engineering, the measures are used to control the quality of the software product and better manage development projects to control the cost of production.</span><span lang="EN-US">In this article we proposed firstly models and measures to evaluate and analyze the complexity of the enterprise architecture and especially the heterogeneity of components and relationships, and secondely we developed a model to automatically detect the change of measures and their impact on enterprise architecture.</span></p>