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Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem…

Optimization and Control · Mathematics 2022-11-22 Zhi Chen , Daniel Kuhn , Wolfram Wiesemann

The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. It is assumed that the pre-change distribution is known (accurately estimated), while the only information about the…

Statistics Theory · Mathematics 2023-09-29 Liyan Xie , Yuchen Liang , Venugopal V. Veeravalli

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…

Optimization and Control · Mathematics 2020-09-22 Polina Alexeenko , Eilyan Bitar

This paper expands the notion of robust profit opportunities in financial markets to incorporate distributional uncertainty using Wasserstein distance as the ambiguity measure. Financial markets with risky and risk-free assets are…

Portfolio Management · Quantitative Finance 2020-06-23 Derek Singh , Shuzhong Zhang

We revisit Markowitz's mean-variance portfolio selection model by considering a distributionally robust version, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures…

Methodology · Statistics 2018-02-15 Jose Blanchet , Lin Chen , Xun Yu Zhou

In this paper, we refine and generalize closed forms for worst-case law invariant convex risk measures with uncertainty sets based on: i) closed balls under $p$-norms and Wasserstein distance; and ii) moment constraints involving mean and…

Risk Management · Quantitative Finance 2025-07-30 Marcelo Righi , Fernanda Müller

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

Robust estimation for modern portfolio selection on a large set of assets becomes more important due to large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance…

Methodology · Statistics 2024-09-12 Ruike Wu , Yanrong Yang , Han Lin Shang , Huanjun Zhu

We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to…

Optimization and Control · Mathematics 2024-07-24 Rui Gao , Rohit Arora , Yizhe Huang

This paper considers structural optimization under a reliability constraint, where the input distribution is only partially known. Specifically, when we only know that the expected value vector and the variance-covariance matrix of the…

Optimization and Control · Mathematics 2022-12-19 Yoshihiro Kanno

Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness w.r.t. the prior distribution. Many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of…

Statistics Theory · Mathematics 2025-09-04 Antonio Di Noia , Fabrizio Ruggeri , Antonietta Mira

We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…

Mathematical Finance · Quantitative Finance 2020-05-27 Stephan Eckstein , Michael Kupper , Mathias Pohl

We develop a novel computationally efficient and general framework for robust hypothesis testing. The new framework features a new way to construct uncertainty sets under the null and the alternative distributions, which are sets centered…

Machine Learning · Statistics 2018-05-29 Rui Gao , Liyan Xie , Yao Xie , Huan Xu

We propose a distributionally robust approach to risk-sensitive estimation of an unknown signal x from an observed signal y. The unknown signal and observation are modeled as random vectors whose joint probability distribution is unknown,…

Machine Learning · Computer Science 2026-04-21 Feras Al Taha , Eilyan Bitar

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

This paper studies distributional model risk in marginal problems, where each marginal measure is assumed to lie in a Wasserstein ball centered at a fixed reference measure with a given radius. Theoretically, we establish several…

Optimization and Control · Mathematics 2023-07-04 Yanqin Fan , Hyeonseok Park , Gaoqian Xu

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…

Machine Learning · Statistics 2024-11-05 Daniel Kuhn , Peyman Mohajerin Esfahani , Viet Anh Nguyen , Soroosh Shafieezadeh-Abadeh

Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…

Machine Learning · Statistics 2024-11-11 Nicola Bariletto , Nhat Ho

We establish a profound connection between coherent risk measures, a prominent object in quantitative finance, and uniform integrability, a fundamental concept in probability theory. Instead of working with absolute values of random…

Risk Management · Quantitative Finance 2025-04-08 Muqiao Huang , Ruodu Wang

Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…

Statistics Theory · Mathematics 2020-12-15 Banghua Zhu , Jiantao Jiao , Jacob Steinhardt