Related papers: Bregman superquantiles. Estimation methods and app…
We consider M-estimators and derive supremal-inequalities of exponential-or polynomial type according as a boundedness- or a moment-condition is fulfilled. This enables us to derive rates of r-complete convergence and also to show r-qick…
We provide a novel criterion for identifying quantum correlation, which allows us to find connections between Bell type inequalities, entanglement detection, and correlation. We utilize the criterion to construct witness operators that can…
When considering d possibly dependent random variables, one is often interested in extreme risk regions, with very small probability p. We consider risk regions of the form ${\mathbf{z}\in\mathbb{R}^d:f(\mathbf{z})\leq\beta}$, where f is…
Bregman divergences generalize measures such as the squared Euclidean distance and the KL divergence, and arise throughout many areas of machine learning. In this paper, we focus on the problem of approximating an arbitrary Bregman…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…
We discuss the use of likelihood asymptotics for inference on risk measures in univariate extreme value problems, focusing on estimation of high quantiles and similar summaries of risk for uncertainty quantification. We study whether…
Measures of accuracy usually score how accurate a specified credence depending on whether the proposition is true or false. A key requirement for such measures is strict propriety; that probabilities expect themselves to be most accurate.…
We consider the problems of estimation and optimization of two popular convex risk measures: utility-based shortfall risk (UBSR) and Optimized Certainty Equivalent (OCE) risk. We extend these risk measures to cover possibly unbounded random…
Recently, a new distance has been introduced for the graphs of two point-to-set operators, one of which is maximally monotone. When both operators are the subdifferential of a proper lower semicontinuous convex function, this distance…
We define a new class of Bayesian point estimators, which we refer to as risk averse. Using this definition, we formulate axioms that provide natural requirements for inference, e.g. in a scientific setting, and show that for well-behaved…
This work introduces a notion of approximate probabilistic trace equivalence for labelled Markov chains, and relates this new concept to the known notion of approximate probabilistic bisimulation. In particular this work shows that the…
Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the…
In the present work, we present numerical results for an iterative method for solving an optimal control problem with inequality contraints. The method is based on generalized Bregman distances. Under a combination of a source condition and…
Large deviation theory has provided important clues for the choice of importance sampling measures for Monte Carlo evaluation of exceedance probabilities. However, Glasserman and Wang [Ann. Appl. Probab. 7 (1997) 731--746] have given…
In this paper, we propose the application of shrinkage strategies to estimate coefficients in the Bell regression models when prior information about the coefficients is available. The Bell regression models are well-suited for modeling…
Conditional value at risk (CVaR) is a popular measure for quantifying portfolio risk. Sensitivity analysis of CVaR is very useful in risk management and gradient-based optimization algorithms. In this paper, we study the infinitesimal…
As a counterpart to the (static) risk measures of generalized quantiles and motivated by Bellini et al. (2018), we propose a new kind of conditional risk measure called conditional generalized quantiles. We first show their well-definedness…
The rough Bergomi model, introduced by Bayer, Friz and Gatheral [Quant. Finance 16(6), 887-904, 2016], is one of the recent rough volatility models that are consistent with the stylised fact of implied volatility surfaces being essentially…
We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision…