Related papers: Star-Shaped deviations
We study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of…
Our paper contributes to the theory of conditional risk measures and conditional certainty equivalents. We adopt a random modular approach which proved to be effective in the study of modular convex analysis and conditional risk measures.…
In this paper we analyze a dynamic recursive extension of the (static) notion of a deviation measure and its properties. We study distribution invariant deviation measures and show that the only dynamic deviation measure which is law…
Elliptically contoured distributions generalize the multivariate normal distributions in such a way that the density generators need not be exponential. However, as the name suggests, elliptically contoured distributions remain to be…
Geometric discrepancies are standard measures to quantify the irregularity of distributions. They are an important notion in numerical integration. One of the most important discrepancy notions is the so-called \emph{star discrepancy}.…
We model a rotating star as a compressible fluid subject to gravitational forces. In almost all the mathematical literature the entropy is considered to be constant. Here we allow it to be variable. We consider a star that steadily rotates…
We present a general framework for a comparative theory of variability measures, with a particular focus on the recently introduced one-parameter families of inter-Expected Shortfall differences and inter-expectile differences, that are…
Risk assessment under different possible scenarios is a source of uncertainty that may lead to concerning financial losses. We address this issue, first, by adapting a robust framework to the class of spectral risk measures. Second, we…
Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not…
We discuss equivalent axiomatic characterizations of distortion risk measures, and give a novel and concise proof of the characterization of elicitable distortion risk measures. Elicitability has recently been discussed as a desirable…
Asteroseismology has emerged as the best way to characterize the global and internal properties of nearby stars. Often, this characterization is achieved by fitting stellar evolution models to asteroseismic observations. The star under…
Monetary risk measures are usually interpreted as the smallest amount of external capital that must be added to a financial position to make it acceptable. We propose a new concept: intrinsic risk measures and argue that this approach…
We analyse the joint distribution of dust attenuation and projected axis ratios, together with galaxy size and surface brightness profile information, to infer lessons on the dust content and star/dust geometry within star-forming galaxies…
Importance sampling has become an important tool for the computation of tail-based risk measures. Since such quantities are often determined mainly by rare events standard Monte Carlo can be inefficient and importance sampling provides a…
Stars of sufficiently low mass are convective throughout their interiors, and so do not possess an internal boundary layer akin to the solar tachocline. Because that interface figures so prominently in many theories of the solar magnetic…
We provide a constructive way of defining new elicitable risk measures that are characterised by a multiplicative scoring function. We show that depending on the choice of the scoring function's components, the resulting risk measure…
We give sufficient conditions for the expected excess and the upper semideviation of recourse functions to be strongly convex. This is done in the setting of two-stage stochastic programs with complete linear recourse and random right-hand…
We introduce adaptive sampling methods for stochastic programs with deterministic constraints. First, we propose and analyze a variant of the stochastic projected gradient method where the sample size used to approximate the reduced…
In this paper, we modify the Bayes risk for the expectile, the so-called variantile risk measure, to better capture extreme risks. The modified risk measure is called the adjusted standard-deviatile. First, we derive the asymptotic…
We propose a novel class of convex risk measures, based on the concept of the Fr\'echet mean, designed in order to handle uncertainty which arises from multiple information sources regarding the risk factors of interest. The proposed risk…