Related papers: Computational aspects of robust optimized certaint…
The aim of this paper is to investigate risk-averse and distributionally robust modeling of Stochastic Optimal Control (SOC) and Markov Decision Process (MDP). We discuss construction of conditional nested risk functionals, a particular…
We consider statistical learning problems in which data are observed as a set of probability measures. Optimal transport (OT) is a popular tool to compare and manipulate such objects, but its computational cost becomes prohibitive when the…
The determination of acceptability prices of contingent claims requires the choice of a stochastic model for the underlying asset price dynamics. Given this model, optimal bid and ask prices can be found by stochastic optimization. However,…
We consider discrete optimization problems with interval uncertatinty of objective function coefficients. The interval uncertainty models measurements errors. A pos\-sible optimal solution is a solution that is optimal for some possible…
This brief note aims to introduce the recent paradigm of distributional robustness in the field of shape and topology optimization. Acknowledging that the probability law of uncertain physical data is rarely known beyond a rough…
We address the statistical estimation of composite functionals which may be nonlinear in the probability measure. Our study is motivated by the need to estimate coherent measures of risk, which become increasingly popular in finance,…
In this paper, we solve the multiple product price optimization problem under interval uncertainties of the price sensitivity parameters in the demand function. The objective of the price optimization problem is to maximize the overall…
Risk measures connect probability theory or statistics to optimization, particularly to convex optimization. They are nowadays standard in applications of finance and in insurance involving risk aversion. This paper investigates a wide…
We study robust versions of pricing problems where customers choose products according to a generalized extreme value (GEV) choice model, and the choice parameters are not known exactly but lie in an uncertainty set. We show that, when the…
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…
While deep learning models often achieve high predictive accuracy, their predictions typically do not come with any provable guarantees on risk or reliability, which are critical for deployment in high-stakes applications. The framework of…
We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here, irreducible uncertainties refers to uncertainties in the…
We consider entropically regularized, semi-discrete versions of variational problems on the set of probability measures involving optimal transport as well as other terms. We prove that the solutions can be characterized by well-posed…
Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…
Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare in a geometrically faithful way point clouds and more generally probability distributions. The wide adoption of OT into existing data analysis and…
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…
This paper develops a risk-adjusted alternative to standard optimal policy learning (OPL) for observational data by importing Roy's (1952) safety-first principle into the treatment assignment problem. We formalize a welfare functional that…
Uncertainty quantification, by means of confidence interval (CI) construction, has been a fundamental problem in statistics and also important in risk-aware decision-making. In this paper, we revisit the basic problem of CI construction,…
Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its…
The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models…