Related papers: The Fatou Closedness under Model Uncertainty
This survey gives an introduction to monetary measures of risk as monotone and cash additive functions on spaces of univariate random variables. Primal and dual representation results as well as several examples are discussed. Principal…
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…
Safe control of constrained linear systems under both epistemic and aleatory uncertainties is considered. The aleatory uncertainty characterizes random noises and is modeled by a probability distribution function (PDF) and the epistemic…
In this manuscript we analyze the weak convergence rate of a discretization scheme for the Heston model. Under mild assumptions on the smoothness of the payoff and on the Feller index of the volatility process, respectively, we establish a…
Input variables in numerical models are often subject to several levels of uncertainty, usually modeled by probability distributions. In the context of uncertainty quantification applied to these models, studying the robustness of output…
The Landau-Pollak uncertainty relation treats a pair of rank one projection valued measures and imposes a restriction on their probability distributions. It gives a nontrivial bound for summation of their maximum values. We give a…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
The notion of quasi-Fej\'er monotonicity has proven to be an efficient tool to simplify and unify the convergence analysis of various algorithms arising in applied nonlinear analysis. In this paper, we extend this notion in the context of…
We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…
This article presents a deep investigation of fixed points for multivalued weak contractions in cone metric spaces. We extend Berinde weak contraction principles to the multivalued setting in cone metric spaces, developing existence,…
Nearly convex sets play important roles in convex analysis, optimization and theory of monotone operators. We give a systematic study of nearly convex sets, and construct examples of subdifferentials of lower semicontinuous convex functions…
A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010) [Asimit, V., Furman, E. and Vernic, R. (2010) On a…
Necessary and sufficient conditions for weak and vague convergence of measures are important for a diverse host of applications. This paper aims to give a comprehensive description of the relationship between the two modes of convergence…
We generalize Lyapunov's convexity theorem for classical (scalar-valued) measures to quantum (operator-valued) measures. In particular, we show that the range of a nonatomic quantum probability measure is a weak*-closed convex set of…
Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…
An elementary application of Fatou's lemma gives a strengthened version of the monotone convergence theorem. We call this the convergence from below theorem. We make the case that this result should be better known, and deserves a place in…
We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai and Fukasawa (2014). The upper and lower bounds of a good…
By making use of the familiar Mathieu series and its generalizations, the authors derive a number of new integral representations and present a systematic study of probability density functions and probability distributions associated with…
We investigate the problem of estimating geodesic tortuosity and constrictivity as two structural characteristics of stationary random closed sets. They are of central importance for the analysis of effective transport properties in porous…
The paper concerns the probabilistic evaluation of plans in the presence of unmeasured variables, each plan consisting of several concurrent or sequential actions. We establish a graphical criterion for recognizing when the effects of a…