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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A fully backward representation of semilinear PDEs applied to the control of thermostatic loads in power systems.

Demand-side management, HJB equation, Ornstein-Uhlenbeck processes, Probabilistic representation of PDEs, Regression Monte-Carlo scheme, Stochastic control, Time-reversal of diffusion

Hedging Expected Losses on Derivatives in Electricity Futures Markets.

Electricity markets, HJB equation, Loss control, Numerical scheme, Partial hedging, Stochastic target

McKean Feynman-Kac probabilistic representations of non-linear partial differential equations.

Backward diffusion, Feynman-Kac measures, HJB equation, McKean stochastic differential equation, Probabilistic representation of PDEs, Time reversed diffusion

Hedging Expected Losses on Derivatives in Electricity Futures Markets.

Electricity markets, HJB equation, Loss control, Numerical scheme, Partial hedging, Stochastic target

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