Related papers: Robust risk measures: an averaging approach

This paper investigates arbitrage properties of financial markets under distributional uncertainty using Wasserstein distance as the ambiguity measure. The weak and strong forms of the classical arbitrage conditions are considered. A…

In this paper, we develop efficient randomized algorithms for estimating probabilistic robustness margin and constructing robustness degradation curve for uncertain dynamic systems. One remarkable feature of these algorithms is their…

We refer to recent inference methodology and formulate a framework for solving the distributionally robust optimization problem, where the true probability measure is inside a Wasserstein ball around the empirical measure and the radius of…

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…

Despite the growing prevalence of artificial neural networks in real-world applications, their vulnerability to adversarial attacks remains a significant concern, which motivates us to investigate the robustness of machine learning models.…

Models continue to increase their already broad use across industry as well as their sophistication. Worldwide regulation oblige financial institutions to manage and address model risk with the same severity as any other type of risk, which…

Optimization of conditional convex risk measure is a central theme in dynamic portfolio selection theory, which has not yet systematically studied in the previous literature perhaps since conditional convex risk measures are neither random…

We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for processes as introduced in Cheridito, Delbaen, and Kupper (2006). These risk measures take into account not only the amounts but also the…

In this paper we study set convergence aspects for Banach spaces of vector-valued measures with divergences (represented by measures or by functions) and applications. We consider a form of normal trace characterization to establish…

The risk of financial positions is measured by the minimum amount of capital to raise and invest in eligible portfolios of traded assets in order to meet a prescribed acceptability constraint. We investigate nondegeneracy, finiteness and…

Robustness analysis is an emerging field in the domain of uncertainty quantification. It consists of analysing the response of a computer model with uncertain inputs to the perturbation of one or several of its input distributions. Thus, a…

We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…

Well-known for its simplicity and effectiveness in classification, AdaBoost, however, suffers from overfitting when class-conditional distributions have significant overlap. Moreover, it is very sensitive to noise that appears in the…

In this note we consider a system of financial institutions and study systemic risk measures in the presence of a financial market and in a robust setting, namely, where no reference probability is assigned. We obtain a dual representation…

In this paper, we study dependence uncertainty and the resulting effects on tail risk measures, which play a fundamental role in modern risk management. We introduce the notion of a regular dependence measure, defined on multi-marginal…

We show that a wide class of risk-constrained nonconvex functional optimization problems exhibit strong duality, regardless of nonconvexity. We develop two novel results under distinct sets of assumptions, establishing strong duality over…

A policy is said to be robust if it maximizes the reward while considering a bad, or even adversarial, model. In this work we formalize two new criteria of robustness to action uncertainty. Specifically, we consider two scenarios in which…

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…

This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…

A sensor has the ability to probe its surroundings. However, uncertainties in its exact location can significantly compromise its sensing performance. The radius of robust feasibility defines the maximum range within which robust…