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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BSDEs with weak terminal condition.

Backward stochastic differential equations, Optimal control, Stochastic target

BSDEs with weak terminal condition.

Backward stochastic differential equations, Optimal control, Stochastic target

Stratified regression Monte-Carlo scheme for semilinear PDEs and BSDEs with large scale parallelization on GPUs.

Backward stochastic differential equations, CUDA, Dynamic programming equation, Em-pirical regressions, GPUs, Parallel computing

Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression.

Backward stochastic differential equations, Dynamic programming equation, Empirical regressions, Malliavin calculus, Non-asymptotic error estimates

Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations.

Backward stochastic differential equations, Empirical regressions, Importance sampling

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

A parallel algorithm for solving BSDEs.

Backward stochastic differential equations, High performance computing, Monte-Carlo methods, Parallel computing

Reflected BSDEs and robust optimal stopping for dynamic risk measures with jumps.

Backward stochastic differential equations, Jump processes, Optimal stopping, Reflected backward stochastic equations, Risk-measures

Game Options in an Imperfect Market with Default.

Backward stochastic differential equations, Doubly reflected backward stochastic differential equations, Game options, Generalized Dynkin games, Imperfect markets, Nonlinear expectations, Nonlinear pricing, Superhedging price

Probabilistic representation of HJB equations for optimal control of jump processes, EDSR (stochastic backward differential equations) and stochastic calculus.

Backward stochastic differential equations, Contrôle optimal, Equations d'Hamilton-Jacobi-Bellman, Equations différentielles stochastiques rétrogrades, Hamilton-Jacobi-Bellman equations, Mesures aléatoires et compensateurs, Optimal control, Piecewise deterministic Markov processes, Processus de Dirichlet au sens faible, Processus de Markov déterministes par morceaux, Random measures and compensators, Weak Dirichlet processes

Stochastic methods in molecular dynamics.

Backward stochastic differential equations, Divergence form operator, Dynamique moléculaire, Molecular dynamic, Opérateur sous forme divergence, Poisson-Boltzmann equation, Équation de Poisson-Boltzmann, Équations différentielles stochastiques rétrogrades

Large Deviations for Non-Markovian Diffusions and a Path-Dependent Eikonal Equation.

Backward stochastic differential equations, Large deviations, Viscosity solutions of path dependent PDEs