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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Hamilton–Jacobi equations for optimal control on junctions and networks.

Hamilton-Jacobi equations, Networks, Optimal control, Viscosity solutions

Hamilton-Jacobi Equations on Networks as Limits of Singularly Perturbed Problems in Optimal Control: Dimension Reduction.

Dimension reduction, Graphs, Hamilton-Jacobi equations, Networks, Optimal control, Singular perturbation, Viscosity solutions

Stochastic homogenization of some interface propagation problems.

Approximation numérique, Contrôle optimal, Equations de Hamilton-Jacobi, Front propagation, Hamilton-Jacobi equations, Homogénéisation stochastique, Metric problem, Numerical approximation, Optimal control, Problème métrique, Propagations de fronts, Stochastic homogenization, Viscosity solutions

Hamilton-Jacobi equations constrained on networks.

Graphs, Hamilton-Jacobi equations, Networks, Optimal control, Viscosity solutions

Contribution to nonlinear and nonlocal partial differential equations and application to road traffic.

Equations non-locales, Homogenization, Homogénéisation, Macroscopic models, Microscopic models, Modèles macroscopiques, Modèles microscopiques, Specified homogenization, Traffic flow, Viscosity solutions

Homogenization and Enhancement of theG-Equation in Random Environments.

Ergodic media, Hamilton-Jacobi equations, Homogenization, Viscosity solutions

Study of numerical methods for partial hedging and switching problems with costs uncertainty.

Contrôle optimal stochastique, Enlargement of filtration, Grilles Sparses, Grossissement de filtration, Mesures de risque (finances), Monotone finite difference schemes, Non-Linear partial differential equations (PDEs), Obliquely reflected backward stochastic differential equations (BSDEs), Optimal Switching, Quantile hedging, Risk measures, Schémas de différences finies monotones, Sparse grids, Stochastic optimal control, Switching optimal, Viscosity solutions, Équations différentielles stochastiques rétrogrades obliquement réfléchies

On a class of path-dependent singular stochastic control problems.

Constrained BSDEs, Path-dependent PDEs, Regularity, Singular control, Transaction costs, Viscosity solutions

Stochastic control and numerical methods in mathematical finance.

BSDE, Calcul de Malliavin, Contrôle stochastique, EDSR, Estimation non-paramétrique, Financial mathematics, Jump processes, Malliavin calculus, Mathématiques financières, Monte Carlo simulations, Non-parametric estimation, Processus a sauts, Simulations Monte Carlo, Solutions de viscosité, Stochastic control, Viscosity solutions

Journey to the heart of second-order EDSRs and other contemporary problems in financial mathematics.

American options, Analyse stochastique quasi-sûre, Asymptotic expansions, Bank monitoring, CDS, CDSs, Développements asymptotiques, EDP complètement non-linéaires, Formule de Feynman-Kac non-linéaire, Fully non-linear PDEs, Générateur à croissance linéaire, Générateur à croissance quadratique, HJB equation, Incertitude de volatilité, Linear growth generator, Liquidity, Liquidité, Maximisation d’utilité robuste, Mesures de probabilité singulières, Non-linear Feynman-Kac formula, Obstacle problem, Options Américaines, Principal/agent problem, Problème d’obstacle, Problème principal/agent, Quadratic growth generator, Quasi-sure stochastic analysis, Robust utility maximization, Second order backward stochastic differential equations, Singular probability measures, Solutions de viscosité, Super-replication, Surréplication, Surveillance des banques, Viscosity solutions, Volatility uncertainty, Équation de HJB, Équations différentielles stochastiques rétrogrades du second ordre

An Overview of Viscosity Solutions of Path-Dependent PDEs.

Optimal stopping, Path-dependent PDEs, Viscosity solutions

An overview of Viscosity Solutions of Path-Dependent PDEs.

Optimal stopping, Path-dependent PDEs, Viscosity solutions