Related papers: An optimal transport foundation for a class of dyn…
We consider a finite horizon stochastic optimal control problem for nearest-neighbor random walk $\{X_i\}$ on the set of integers. The cost function is the expectation of exponential of the path sum of a random stationary and ergodic…
This paper investigates risk measures derived from the expected maximum deficit in a continuous-time framework and develops optimal reserve allocation strategies across multiple lines of business. We formalize the expected maximum deficit…
In this paper, we propose a risk-based data-driven approach to optimal power flow (DROPF) with dynamic line rating. The risk terms, including penalties for load shedding, wind generation curtailment and line overload, are embedded into the…
Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…
Safe navigation in real-time is challenging because engineers need to work with uncertain vehicle dynamics, variable external disturbances, and imperfect controllers. A common safety strategy is to inflate obstacles by hand-defined margins.…
We study dynamic risk measures in a very general framework enabling to model uncertainty and processes with jumps. We previously showed the existence of a canonical equivalence class of probability measures hidden behind a given set of…
Given a smooth Riemannian manifold $(M,g)$, compact and without boundary, we analyze the dynamical optimal mass transport problem where the cost is given by the sum of the kinetic energy and the relative entropy with respect to a reference…
We develop an approach to time-consistent risk evaluation of continuous-time processes in Markov systems. Our analysis is based on dual representation of coherent risk measures, differentiability concepts for multivalued mappings, and a…
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…
Safe corridor-based Trajectory Optimization (TO) presents an appealing approach for collision-free path planning of autonomous robots, offering global optimality through its convex formulation. The safe corridor is constructed based on the…
Weak optimal transport generalizes the classical theory of optimal transportation to nonlinear cost functions and covers a range of problems that lie beyond the traditional theory - including entropic transport, martingale transport, and…
Recently, literature on dynamic coherent risk measures has broadened the choices for risk-sensitive performance evaluation. A running example includes Cumulative prospect theory and Conditional variance at risk. Most of them can be can be…
Conditional risk minimization arises in high-stakes decisions where risk must be assessed in light of side information, such as stressed economic conditions, specific customer profiles, or other contextual covariates. Constructing reliable…
The nonequilibrium short-time critical behaviors of driven and undriven lattice gases are investigated via Monte Carlo simulations in two spatial dimensions starting from a fully disordered initial configuration. In particular, we study the…
In the classical static optimal reinsurance problem, the cost of capital for the insurer's risk exposure determined by a monetary risk measure is minimized over the class of reinsurance treaties represented by increasing Lipschitz retained…
Generalization methods offer a powerful solution to one of the key drawbacks of randomized controlled trials (RCTs): their limited representativeness. By enabling the transport of treatment effect estimates to target populations subject to…
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…
Series of univariate distributions indexed by equally spaced time points are ubiquitous in applications and their analysis constitutes one of the challenges of the emerging field of distributional data analysis. To quantify such…
Choosing a portfolio of risky assets over time that maximizes the expected return at the same time as it minimizes portfolio risk is a classical problem in Mathematical Finance and is referred to as the dynamic Markowitz problem (when the…
The dynamical formulation of optimal transport, also known as Benamou-Brenier formulation or Computational Fluid Dynamics formulation, amounts to write the optimal transport problem as the optimization of a convex functional under a PDE…