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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Levy process and American options.

American options, Cva, Exponetial Levy model, Free boundary, Inéquation variationnelle, Modèles exponentiels de Lévy, Options américaines, Région d\'exercice, Vitesse de convergence du prix critique

Stochastic approximations for financial risk computations.

American options, Approximation faibles, Credit risk measures, Décomposition en polynômes du chaos, Forward Variance, Initial Margin, Marge Initiale, Mesures de risque de crédit, Meta-modeling, Monte Carlo multi-Niveaux, Multilevel Monte Carlo, Métamodélisation, Options américaines, Orthogonal polynomials, Polynomial Chaos Expansion, Polynômes orthogonaux, Risk management, VIX, Variance Forward, Weak approximations

The Parareal Algorithm for American Options.

American options, Financial securities, LSMC, Parareal, Risk assessment

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

American options in a non-linear incomplete market model with default.

American options, Constrained reflected BSDE, Control problems with non-linear expectation, F-expectation, Incomplete markets, Non-linear optional decomposition, Non-linear pricing, Optimal stopping with non-linear expectation, Pricing-hedging duality

Superhedging prices of European and American options in a non-linear incomplete market with default.

American options, BSDEs with constraints, Constrained reflected BSDEs, Control problems with non-linear expectation, European options, F -expectation, Incomplete markets, Non-linear optional decomposition, Non-linear pricing, Optimal stopping with non-linear expectation, Pricing-hedging duality

American options in an imperfect complete market with default.

American options, Default, Imperfect markets, Nonlinear expectation, Reflected backward stochastic differential equations, Superhedging

Study of two stochastic control problems: American put with discrete dividends and dynamic programming principle with constraints in probabilities.

American Options, Contrôle optimal stochastique, Dividendes, Dividends, Dynamic programming, Exercise boundary, Frontière d\'exercice, Lévy processes, Options Américaines, Processus de Lévy, Programmation dynamique, Stochastic optimal control

Volterra process and applications in finance.

American options, Option Américaine, Processus de Volterra, Rough volatility, Volatilité rugueuse, Volterra processes