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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Chernoff’s density is log-concave.

Brownian motion, Polya frequency function, Prekopa–Leindler theorem, Schoenberg’s theorem, airy function, correlation inequalities, hyperbolically monotone, log-concave, monotone function estimation, slope process, strongly log-concave

On logarithmic Sobolev inequalities for the heat kernel on the Heisenberg group.

Brownian Motion, Central Limit Theorem, Heat kernel, Heisenberg group, Logarithmic Sobolev inequality, Poincaré inequality, Random Walk

On the expectation of normalized Brownian functionals up to first hitting times.

Bessel process, Brownian meander, Brownian motion, Feynman-Kac formula, Hitting times, Random sampling, Ray-Knight theorem, Scaling

On the expectation of normalized Brownian functionals up to first hitting times.

Bessel process, Brownian meander, Brownian motion, Feynman-Kac formula, Hitting times, Random sampling, Ray-Knight theorem, Scaling

Dependence modeling between continuous time stochastic processes : an application to electricity markets modeling and risk management.

Bandwidth selection, Brownian motion, Copula, Copule, Dependence, Dépendance, Electricity markets, Estimateur à polynômes locaux, Estimation non paramétrique, Finance mathématique, Gestion des risques, High frequency statistics, Intensité stochastique, Inégalité oracle, Local polynomial estimation, Marchés de l'électricité, Mathematical finance, Mouvement Brownien, Non parametric estimation, Oracle inequality, Pics, Poisson process, Processus de Poisson, Production éolienne, Risk management, Semimartingale, Spikes, Statistique haute fréquence, Stochastic intensity, Sélection de fenêtre, Wind production

Functional quantization-based stratified sampling methods.

Brownian bridge, Brownian motion, Functional quantization, Gaussian process, Karhunen-Loève, Monte Carlo, Numerical integration, Option pricing, Ornstein-Uhlenbeck bridge, Ornstein-Uhlenbeck process, Path-dependent option, Principal component analysis, Product quantizer, Stratification, Variance reduction, Vector quantization, Voronoi diagram

Singular mean-field control games.

Brownian motion, Mean-field stochastic differential equations, Nash equilibrium, Optimal singular control, Poisson random measures, Singular mean-field control games, Skorohod reflection problem, Stochastic maximum principles

A Simple GDP-based Model for Public Investments at Risk.

Brownian motion, Decision making, Discount rate, Investment, Risk, Risk and uncertainty

On the Law of a Triplet Associated with the Pseudo-Brownian Bridge.

Bessel process, Brownian motion, Hitting times, Local time, Mellin transform, Pseudo-Brownian bridge, Scaling, Uniform sampling

On the law of a triplet associated with the pseudo-Brownian bridge.

Bessel process, Brownian motion, Hitting times, Local time, Mellin transform, Pseudo-Brownian bridge, Scaling, Uniform sampling

The density of a passage time for a renewal-reward process perturbed by a diffusion.

Brownian motion, Jump-diffusion process, Renewal-reward process, Time of ruin

Dependence modeling between continuous time stochastic processes : an application to electricity markets modeling and risk management.

Bandwidth selection, Brownian motion, Copula, Copule, Dependence, Dépendance, Electricity markets, Estimateur à polynômes locaux, Estimation non paramétrique, Finance mathématique, Gestion des risques, High frequency statistics, Intensité stochastique, Inégalité oracle, Local polynomial estimation, Marchés de l'électricité, Mathematical finance, Mouvement Brownien, Non parametric estimation, Oracle inequality, Pics, Poisson process, Processus de Poisson, Production éolienne, Risk management, Semimartingale, Spikes, Statistique haute fréquence, Stochastic intensity, Sélection de fenêtre, Wind production