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).


Reset

An application of the KMT construction to the pathwise weak error in the Euler approximation of one-dimensional diffusion process with linear diffusion coefficient.

Diffusion process, Euler scheme, Komlós -Major- Tusnády construction, Wasserstein couplings

Approximation and density estimation for stochastic evolution equations.

Calcul de Malliavin, Euler scheme, Malliavin calculus, Schéma d’Euler, Stochastic differential equations, Équation de la chaleur, Équation différentielle stochastique

First time to exit of a continuous Itô process: General moment estimates and ${\mathrm{L}}_{1}$-convergence rate for discrete time approximations.

Euler scheme, Exit time, Strong approximation

Multilevel Richardson–Romberg extrapolation.

Euler scheme, Multi-Step, Multilevel Monte Carlo methods, Nested Monte Carlo method, Option pricing, Richardson-Romberg Extrapolation, Stratification

Invariant measure of duplicated diffusions and application to Richardson–Romberg extrapolation.

Asymptotic flatness, Central Limit Theorem, Confluence, Ergodic diffusion, Euler scheme, Gradient System, Hypoellipticity, Invariant measure, Lyapunov exponent, Optimal transport, Richardson-Romberg extrapolation, Two-point motion

Limit theorems for weighted and regular Multilevel estimators.

Central Limit Theorem, Euler scheme, Law of large numbers, Multilevel Monte Carlo methods, Nested Monte Carlo, Richardson- Romberg extrapolation

Acceleration of the Monte Carlo method for diffusion processes and applications in Finance.

Esscher transform, Euler scheme, Financial mathematics, Heston model, Mathématiques financières, Modèle de Heston, Robbins-Monro, Schéma d'Euler, Transformation d'Esscher

A mixed-step algorithm for the approximation of the stationary regime of a diffusion.

Central Limit Theorem, Ergodic diffusion, Euler scheme, Poisson equation, Stationary process, Steady regime, Stochastic differential equation

Vibrato and Automatic Differentiation for High Order Derivatives and Sensitivities of Financial Options.

Automatic Differentiation, Euler Scheme, Greeks, High Dimension, High Order Derivative, Monte Carlo Method, Option Pricing, Path-Dependent Option, Vibrato

Non-asymptotic error bounds for the multilevel Monte Carlo Euler method applied to SDEs with constant diffusion coefficient.

Euler scheme, Malliavincalculus, Multilevel Monte Carlo methods, Non asymptotic bounds

Importance Sampling and Statistical Romberg method.

Central limit theorem, Euler scheme, Heston model, Robbins-Monro, Statistical Romberg method, Stochastic algorithm, Variance reduction

Numerical computation for backward doubly SDEs with random terminal time.

And phrases Backward Doubly Stochastic Differential Equation, Dirichlet condition, Euler scheme, Exit time, Method, Monte carlo, SPDEs, Stochastic flow