One of the mantras risk measurement is avoidance concentration. However, most formal approaches to topic actually require more than this. In “Star-Shaped Risk Measures,” Castagnoli, Cattelan, Maccheroni, Tebaldi, and Wang study this property “in purity” for monetary measures. They show that it unites value at convex measures, amenable aggregation opinions, leads treatable optimization, thanks a...

The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is crucial importance making well-informed decisions. In this paper, we quantify, for the class distortion with an absolutely continuous function, its distributional uncertainty by deriving largest (smallest) value when distribution has a known mean and variance and, furthermore, lies within...

Background: The predictive power of obesity measures varies according to the presence of coexistent measures. The present study aimed to determine the predictive power of combinations of obesity measures for diabetes by calculation of a linear risk score. Methods: Data from a population-based cross-sectional study of 994 representative samples of Iranian adults in Babol, Iran were analyzed. Me...

Part of the course was devoted to an analysis of Value at Risk and its relation to quantiles. A detailed discussion of this can be found in two papers by Artzner, Delbaen, Eber and Heath, ADEH1 and ADEH2. It will not be repeated here. We will rather concentrate on the mathematics behind the concept of coherent risk measures. They were introduced in the two mentioned papers and the mathematical ...