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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From Boltzmann to random matrices and beyond.

Boltzmann, Central limit theorem, Circular law, Collective phenomena, Coulomb gas, Diffusion processes, Electrostatics, Entropy, Equilibrium measure, Fisher information, Free probability, Ginibre ensemble, Interacting Particle Systems, Large Deviations Principle, Markov processes, Mean-field interaction, Potential theory, Random matrices, Riesz kernel, Shannon, Singular repulsion, Voiculescu

First-order global asymptotics for confined particles with singular pair repulsion.

Coulomb interaction, Equilibrium measure, Interacting particle systems, Large deviations, Mean field limit, Potential theory, Riesz kernel

Study of new rare event simulation schemes and their application to extreme scenario generation.

Ergodic properties, Extreme scenario, Interacting particle systems, Markov chains, Rare event

Rare event simulation related to financial risks: efficient estimation and sensitivity analysis.

Credit default swaps, Deep out-of-the-money options, Ergodic properties, Fractional Brownian motion, Interacting particle systems, Malliavin calculus, Markov chains, Model misspecification, Monte Carlo simulation, Rare event, Sensitivity analysis

Stochastic local intensity loss models with interacting particle systems.

Credit derivatives, Fokker-Planck equation, Interacting particle systems, Loss modelling, Martingale problem, Monte-Carlo Algorithm, Stochastic local intensity model

Weak error analysis of time and particle discretization of nonlinear stochastic differential equations in the McKean sense.

Analyse de l'erreur faible, Diffusions non linear in the sense of McKean, Diffusions non linéaires au sens de McKean, Euler-Maruyama scheme, Interacting particle systems, Interaction à champ moyen, Mean-Field interaction, Propagation du chaos, Propagation of chaos, Schéma d'Euler-Maruyama, Systèmes de particules en interaction, Weak error analysis

Probabilistic study of interacting particle systems: applications to molecular simulation.

Calculs d'énergies libres, Free energy calculations, Hyperbolic conservation laws, Interacting particle systems, Interprétation probabiliste des équations aux dérivées partielles, Lois de conservation hyperboliques, Lévy processes, Méthodes de Monte Carlo en chimie quantique, Probabilistic interpretation of partial differential equations, Processus de Lévy, Quantum Monte Carlo methods, Systèmes de particules en intéraction

Numerical Computations for Backward Doubly Stochastic Differential Equations and Nonlinear Stochastic PDEs.

Algorithme de Hastings- Metropolis, Backward Doubly Stochastic Differential Equations, Chaînes dee Markov, Equations aux dérivées partielles stochastiques nonlinéaires, Equations différentielles doublement stochastiques rétrogrades, Generalized Backward Doubly Stochastic Differential Equations, Hastings-Metropolis algorithm, Interacting particle systems, Markov chains, Monte-Carlo simulations, Projections, Quasilinear Stochastic PDEs, Régression, Semilinear Stochastic PDEs, Simulations de Monte-Carlo, Système de particules en intéraction