Related papers: Data-driven Multiperiod Robust Mean-Variance Optim…
We present a framework to simultaneously align and smooth data in the form of multiple point clouds sampled from unknown densities with support in a d-dimensional Euclidean space. This work is motivated by applications in bioinformatics…
The classical mean-variance portfolio selection problem induces time-inconsistent (precommited) strategies (see Zhou and Li (2000)). To overcome this time-inconsistency, Basak and Chabakauri (2010) introduce the game theoretical approach…
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…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
We study the feasibility and noise sensitivity of portfolio optimization under some downside risk measures (Value-at-Risk, Expected Shortfall, and semivariance) when they are estimated by fitting a parametric distribution on a finite sample…
We present a novel approach for the control of uncertain, linear time-invariant systems, which are perturbed by potentially unbounded, additive disturbances. We propose a \emph{doubly robust} data-driven state-feedback controller to ensure…
We present a methodology for predictable and safe covariance steering control of uncertain nonlinear stochastic processes. The systems under consideration are subject to general uncertainties, which include unbounded random disturbances…
We develop a notion of projections between sets of probability measures using the geometric properties of the 2-Wasserstein space. It is designed for general multivariate probability measures, is computationally efficient to implement, and…
Portfolio selection in the periodic investment of securities modeled by a multivariate Merton model with dependent jumps is considered. The optimization framework is designed to maximize expected terminal wealth when portfolio risk is…
Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted…
We study an optimization-based approach to con- struct a mean-reverting portfolio of assets. Our objectives are threefold: (1) design a portfolio that is well-represented by an Ornstein-Uhlenbeck process with parameters estimated by maximum…
The aim of this paper is to address the challenge of gradual domain adaptation within a class of manifold-constrained data distributions. In particular, we consider a sequence of $T\ge2$ data distributions $P_1,\ldots,P_T$ undergoing a…
Despite half a century of research, there is still no general agreement about the optimal approach to build a robust multi-period portfolio. We address this question by proposing the detrended cluster entropy approach to estimate the…
Distributionally Robust Optimization (DRO) has enabled to prove the equivalence between robustness and regularization in classification and regression, thus providing an analytical reason why regularization generalizes well in statistical…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…
The debate between active and passive investment strategies has been ongoing for many years and is far from being over. In this paper, we show that the choice of an optimal portfolio management strategy depends on an investment climate,…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…
We propose a scalable robust learning algorithm combining kernel smoothing and robust optimization. Our method is motivated by the convex analysis perspective of distributionally robust optimization based on probability metrics, such as the…
Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…