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In decision making under uncertainty and risk, worst-case risk assessments are often conducted using maxitive monetary risk measures. In this article, we study maxitive monetary risk measures on the space $L^0$ of all random variables…

Probability · Mathematics 2025-04-16 José Miguel Zapata

We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic…

Machine Learning · Computer Science 2021-06-14 Zifan Liu , Jongho Park , Theodoros Rekatsinas , Christos Tzamos

Distributionally Robust Optimization (DRO) is a worst-case approach to decision making when there is model uncertainty. It is also well known that for certain uncertainty sets, DRO is approximated by a regularized nominal problem. We show…

Optimization and Control · Mathematics 2026-05-08 Jun-ya Gotoh , Michael Jong Kim , Andrew E. B. Lim

We extend the scope of risk measures for which backtesting models are available by proposing a multinomial backtesting method for general distortion risk measures. The method relies on a stratification and randomization of risk levels. We…

Risk Management · Quantitative Finance 2024-08-02 Sören Bettels , Sojung Kim , Stefan Weber

We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…

Optimization and Control · Mathematics 2021-06-09 Mert Gürbüzbalaban , Andrzej Ruszczyński , Landi Zhu

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…

Mean-deviation models, along with the existing theory of coherent risk measures, are well studied in the literature. In this paper, we characterize monotonic mean-deviation (risk) measures from a general mean-deviation model by applying a…

Risk Management · Quantitative Finance 2024-08-12 Xia Han , Ruodu Wang , Qinyu Wu

Rare events, and more general risk-sensitive quantities-of-interest (QoIs), are significantly impacted by uncertainty in the tail behavior of a distribution. Uncertainty in the tail can take many different forms, each of which leads to a…

Probability · Mathematics 2019-11-22 Jeremiah Birrell , Paul Dupuis , Markos A. Katsoulakis , Luc Rey-Bellet , Jie Wang

We present a distribution optimization framework that significantly improves confidence bounds for various risk measures compared to previous methods. Our framework encompasses popular risk measures such as the entropic risk measure,…

Machine Learning · Computer Science 2023-06-13 Hao Liang , Zhi-quan Luo

Circular variables that represent directions or periodic observations arise in many fields, such as biology and environmental sciences. An important issue when dealing with circular data is how to estimate their dispersion robustly,…

Methodology · Statistics 2026-03-03 Houyem Demni , Mia Hubert , Giovanni C. Porzio , Peter J. Rousseeuw

The paper studies the robustness properties of discrete-time stochastic optimal control under Wasserstein model approximation for both discounted-cost and average-cost criteria. Specifically, we study the performance loss when applying an…

Systems and Control · Electrical Eng. & Systems 2026-03-10 Yichen Zhou , Yanglei Song , Serdar Yüksel

We discuss recently developed methods that quantify the stability and generalizability of statistical findings under distributional changes. In many practical problems, the data is not drawn i.i.d. from the target population. For example,…

Methodology · Statistics 2023-10-05 Dominik Rothenhäusler , Peter Bühlmann

Distributionally robust optimization has emerged as an attractive way to train robust machine learning models, capturing data uncertainty and distribution shifts. Recent statistical analyses have proved that generalization guarantees of…

Optimization and Control · Mathematics 2025-01-28 Tam Le , Jérôme Malick

We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where…

Optimization and Control · Mathematics 2020-12-17 Ashish Cherukuri , Ashish R. Hota

We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning…

Statistics Theory · Mathematics 2021-08-05 Jose Blanchet , Karthyek Murthy , Viet Anh Nguyen

In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…

Systems and Control · Electrical Eng. & Systems 2025-06-13 Eduardo Figueiredo , Steven Adams , Peyman Mohajerin Esfahani , Luca Laurenti

We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…

Machine Learning · Statistics 2020-02-10 Muhammad Osama , Dave Zachariah , Peter Stoica

Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is…

Risk Management · Quantitative Finance 2018-02-12 Valeria Bignozzi , Claudio Macci , Lea Petrella

In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…

Optimization and Control · Mathematics 2023-09-07 Romain Guillaume , Adam Kasperski , Pawel Zielinski

We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization. We model uncertainty in terms of the Gelbrich distance on the mean-covariance space, along with prior structural information about…

Portfolio Management · Quantitative Finance 2025-10-02 Viet Anh Nguyen , Soroosh Shafiee , Damir Filipović , Daniel Kuhn