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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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

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

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

Variational methods for Hamilton-Jacobi equations and applications.

Augmented Lagrangian, Dualité de Fenchel-Rockafellar, Fenchel-Rockafellar duality, Hamilton-Jacobi equations, Lagrangien augmenté, Optimal transport, Shape from Shading, Transport optimal, Équations d’Hamilton-Jacobi

Three essays on modeling dependence between financial assets.

Copules, Couplage de processus stochastiques, Dépendance extrème, Dépendances entre vecteurs aléatoires, Transport optimal

Quantification of the model risk in finance and related problems.

Backward stochastic differential equations, Couverture quadratique, Equations différentielles stochastiques rétrogrades, Gas storage unit, Martingale problem, Model risk, Optimal transport, Problème martingale, Quadratic hedging, Risque de modèle, Transport optimal, Unité de stockage de gaz

Optimal transport in high dimension : obtaining regularity and robustness using convexity and projections.

Apprentissage statistique, Machine Learning, Machine learning, Optimal transport, Statistical Learning, Transport optimal

Statistics on topological descriptors based on optimal transport.

Algorithmes, Algorithms, Analyse topologique des données, Barycenters, Barycentres, Convergence de mesures positives, Convergence of nonnegative measures, Diagrammes de persistance, Optimal transport, Persistence diagrams, Topological data analysis, Transport optimal