Related papers: Law-Invariant Return and Star-Shaped Risk Measures
This paper presents relations between several types of closedness of a law-invariant convex set in a rearrangement invariant space $\mathcal{X}$. In particular, we show that order closedness,…
This paper proposes a unified framework for the investigation of constrained learning theory in reflexive Banach spaces of features via regularized empirical risk minimization. The focus is placed on Tikhonov-like regularization with…
Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…
We characterize several stability properties, such as inverse or composition closedness, for ultraholomorphic function classes of Roumieu type defined in terms of a weight matrix. In this way we transfer and extend known results from J.…
We consider two types of convolutions ($\ast$ and $\star$) of functions on spaces of finite configurations (finite subsets of a phase space), and some their properties are studied. A connection of the $\ast$-convolution with the convolution…
We prove a strengthened form of convexity for operator monotone decreasing positive functions defined on the positive real numbers. This extends Ando and Hiai's work to allow arbitrary positive maps instead of states (or the identity map),…
In this paper, we obtain coefficient criteria for a normalized harmonic function defined in the unit disk to be close-to-convex and fully starlike, respectively. Using these coefficient conditions, we present different classes of harmonic…
This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…
Building on recent developments in models focused on the shape properties of odds ratios, this paper introduces two new models that expand the class of available distributions while preserving specific shape characteristics of an underlying…
In this paper we establish a new characterisation of star-regular categories, using a property of internal reflexive graphs, which is suggested by a recent result due to O. Ngaha Ngaha and the first author. We show that this property is, in…
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…
A variety of real-world applications are modeled via hyperbolic conservation laws. To account for uncertainties or insufficient measurements, random coefficients may be incorporated. These random fields may depend discontinuously on the…
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…
We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the…
Let $\ID$ denote the open unit disk and $f:\,\ID\TO\BAR\IC$ be meromorphic and univalent in $\ID$ with the simple pole at $p\in (0,1)$ and satisfying the standard normalization $f(0)=f'(0)-1=0$. Also, let $f$ have the expansion…
Stable distribution is one of the attractive models that well describes fat-tail behaviors and scaling phenomena in various scientific fields. The approach based upon the method of moments yields a simple procedure for estimating stable law…
This work explores and develops elements of Stein's method of approximation, in the infinitely divisible setting, and its connections to functional analysis. It is mainly concerned with multivariate self-decomposable laws without finite…
The theory of convex risk functions has now been well established as the basis for identifying the families of risk functions that should be used in risk averse optimization problems. Despite its theoretical appeal, the implementation of a…
In the paper we investigate automatic Fatou property of law-invariant risk measures on a rearrangement-invariant function space $\mathcal{X}$ other than $L^\infty$. The main result is the following characterization: Every real-valued,…
A normalized univalent function is uniformly convex if it maps every circular arc contained in the open unit disk with center in it into a convex curve. This article surveys recent results on the class of uniformly convex functions and on…