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This paper discusses a class of combinatorial optimization problems with uncertain costs in the objective function. It is assumed that a sample of the cost realizations is available, which defines an empirical probability distribution for…
In this paper we study a robust expected utility maximization problem with random endowment in discrete time. We give conditions under which an optimal strategy exists and derive a dual representation for the optimal utility. Our approach…
We study the problem of maximising terminal utility for an agent facing model uncertainty, in a frictionless discrete-time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the…
This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent…
As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this…
In this paper we investigate a utility maximization problem with drift uncertainty in a multivariate continuous-time Black-Scholes type financial market which may be incomplete. We impose a constraint on the admissible strategies that…
We consider distributionally robust optimization problems where the uncertainty is modeled via a structured Wasserstein ambiguity set. Specifically, the ambiguity is restricted to product measures $P^{\otimes N}$, where $P$ lies within a…
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 consider the optimal investment and marginal utility pricing problem of a risk averse agent and quantify their exposure to a small amount of model uncertainty. Specifically, we compute explicitly the first-order sensitivity of their…
We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local,…
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…
We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete)…
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…
Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…
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…
We investigate a stochastic program with expected value constraints, addressing the problem in a general context through Distributionally Robust Optimization (DRO) approach using Wasserstein distances, where the ambiguity set depends on the…
This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…
We present a provably safe sampling-based motion planning algorithm for robotic systems affected by random disturbances of unknown distribution. We consider systems with linear or linearizable dynamics evolving in workspace with…
We consider decision-making problems involving the optimization of linear objective functions with uncertain coefficients. The probability distribution of the coefficients--which are assumed to be stochastic in nature--is unknown to the…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…