Research
Publications
Huyên Pham, Xavier Warin, and Maximilien Germain. “Neural networks-based backward scheme for fully non-linear PDEs.” In: SN Partial Differential Equations and Applications 2, 16 (2021). arXiv version published version
Maximilien Germain, Huyên Pham, and Xavier Warin. "Approximation error analysis of some deep backward schemes for nonlinear PDEs ". In: SIAM Journal on Scientific Computing 44.1 (2022), A28–A56. arXiv version published version
Maximilien Germain, Joseph Mikael and Xavier Warin. "Numerical resolution of McKean-Vlasov FBSDEs using neural networks". In: Methodology and Computing in Applied Probability 24, 2557–2586 (2022) arXiv version published version
Maximilien Germain, Mathieu Laurière, Huyên Pham, and Xavier Warin. "DeepSets and their derivative networks for solving symmetric PDEs". In: Journal of Scientific Computing 91, 63 (2022). arXiv version published version
Maximilien Germain, Huyên Pham, and Xavier Warin. "Rate of convergence for particle approximation of PDEs in Wasserstein space". In: Journal of Applied Probability 59.4 (2022). arXiv version published version
Tiziano De Angelis, Maximilien Germain, and Elena Issoglio. "A numerical scheme for stochastic differential equations with distributional drift". In: Stochastic Processes and their Applications 154 (2022) arXiv version published version
Maximilien Germain, Huyên Pham, and Xavier Warin. “Neural networks based algorithms for stochastic control and PDEs in finance”. In: Machine Learning And Data Sciences For Financial Markets: A Guide To Contemporary Practices. Ed. by A. Capponi and C.A. Lehalle. Cambridge University Press, (2023). Chap. New Frontiers for Stochastic Control in Finance. arXiv version published version
Maximilien Germain, Huyên Pham, and Xavier Warin. "A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection" (2022). In: Numerical Algebra, Control and Optimization 13(3&4): 555-582 (2023), special issue Stochastic Analysis, Mathematical Finance, and Related Fields arXiv version published version
Preprints
Noufel Frikha, Maximilien Germain, Mathieu Laurière, Huyên Pham, and Xuanye Song. "Actor-critic learning for mean-field control in continous time" (2023). arXiv version
Thesis documents
Work in progress
Talks
BSDE 2022, June 27 - July 01, 2022, Annecy
45e Congrès National d'Analyse Numérique, June 13 - June 17, 2022, Evian-les-Bains
Groupe de travail finance mathématique, actuariat et probabilités numériques, May 12, 2022, Université Paris Cité
Groupe de Travail Méthodes Stochastiques et Finance, CERMICS Ecole des Ponts et Chaussées, Mar 31, 2022
PGMO Days, Nov 30 - Dec 01, 2021
FIME/FDD workshop, Sep 22 - Sep 23, 2021 slides
European Summer School in Financial Mathematics, Aug 30 - Sep 03, 2021 slides talk recording
Stochastic analysis seminar, ENSTA-CMAP-ENSAE, Oct 19, 2020
ICODE workshop on numerical solution of HJB equations, Jan 8-10 2020
Reviewer for:
SIAM Journal on Scientific Computing
Partial Differential Equations and Applications
MathematicS in Action
Digital Finance
IMA Journal of Numerical Analysis