Patrimony

The Louis Bachelier Group's patrimony has been defined as all the publications produced by academic researchers thanks to Group funding (ILB, FdR, IEF, Labex) or via the use of EquipEx data (BEDOFIH, EUROFIDAI).


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Robust pricing-hedging duality for American options in discrete time financial markets.

60G05, American option, Kantorovich duality, Martingale, Nondominated model, Optimal transport, Secondary 49M29, Super-replication

Optimal curves and applications with values in Wasserstein space.

Analyse dans les espaces métriques, Analysis in metric spaces, Calcul des variations, Calculus of variations, Elliptic regularity, Optimal transport, Régularité elliptique, Transport optimal

Optimal control in Wasserstein spaces.

Alignment problems, Analyse non-Lisse, Calcul sous-Différentiel métrique, Contrôle optimal, Espaces de Wasserstein, Géométrie sous-Riemannienne, Limite de champs moyen, Lipschitz regularity, Mean-Field limit, Multi-Agent systems, Non-Smooth analysis, Optimal control, Optimal transport, Persistance d'excitations, Persistency of excitation, Problèmes d'alignement, Régularité Lipschitz, Singularity theory, Sub-Riemannian geometry, Subdifferential calculus in metric spaces, Systèmes multi-Agents, Théorie des singularités, Transport optimal, Wasserstein spaces

Schrödinger's problem and its links with optimal transport and functional inequalities.

Bakry-Emery, Courbure-dimension, Curvature-dimension, Entropie, Entropy, Functional Inequalities, Inégalités Fonctionnelles, Optimal Transport, Problème de Schrödinger, Schrödinger Problem, Transport Optimal

Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case.

Best-reply iteration, Congestion, Continuum of players, Cournot-Nash equilibria, Non-symmetric interactions, Optimal transport

Systems of interacting particles, gradient flow approach in Wasserstein space.

Augmented lagrangian, Benamou-Brenier formula, Cross-Diffusion, Crowd motions, Diffusions croisées, Diffusions non linéaires, Distance de Wasserstein, Dérive non locale, Espèces en interaction, Flots de gradient, Formule de Benamou-Brenier, Gradient flows, Hele-Shaw equation, Interacting species, JKO scheme, Lagrangien augmenté, Mouvement de foules, Multi-Marginal transport, Nonlinear diffusions, Nonlocal drift, Optimal transport, Reaction-Diffusion systems, Schéma JKO, Splitting, Systèmes de réaction-Diffusion, Transport multi-Marges, Transport optimal, Wasserstein distance, Équations d'Hele-Shaw

Iterative Bregman Projections for Regularized Transportation Problems.

Bregman projection, Entropy, Kulback-Leibler divergence, Optimal transport, Wasserstein barycenters

Numerical Methods for Multi-Marginal Optimal Transportation.

Algorithme de Bregman, Algorithme de Dykstra, Barycentre de Wasserstein, Bregman algorithm, Capacity constraint, Contrainte de capacité, Cournot-Nash, Dft, Dykstra algorithm, Entropic regularization, Euler equations, Fractal map, Map fractale, Multi-Marginal Optimal transport, Optimal transport, Partial transport, Problème de Schrödinger, Régularisation entropique, Schrödinger problem, Tfd, Transport Optimal Multi-Marges, Transport Partiel, Transport optimal, Wasserstein barycenter, Équations d’Euler

Density constraints in optimal transport, PDEs and mean field games.

Contraintes de densité, Density constraints, Jeux à champ moyen, Macroscopic crowd motion models, Mean field games, Modèles macroscopiques de mouvement de foule, Optimal transport, Transport optimal

Optimal multidimensional martingale transport.

Duality, Dualité, Finance robuste, Local structure, Martingale, Numerics, Numérique, Optimal transport, Robust finance, Structure locale, Transport optimal

Convergence of Entropic Schemes for Optimal Transport and Gradient Flows.

Entropic regularization, Gradient flows, Optimal transport

Augmented Lagrangian methods for transport optimization, Mean-Field Games and degenerate PDEs.

Augmented Lagrangian, Degenerate elliptic PDEs, Mean-Field Games, Monge Problem, Optimal Transport