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 (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

  • Maximilien Germain, Huyên Pham, and Xavier Warin. “Neural networks based algorithms for stochastic control and PDEs in finance”. In: to appear 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, (2022). Chap. New Frontiers for Stochastic Control in Finance. arXiv version

Preprints

  • Tiziano De Angelis, Maximilien Germain, and Elena Issoglio. "A numerical scheme for stochastic differential equations with distributional drift". (2019). In: arXiv:1906.11026. Minor revision requested

  • 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" (2021). In: arXiv:2112.11059 Under review

Work in progress


  • Reinforcement Learning for mean-field control.

  • Exploration for mean-field control and master equations.

Talks


Reviewer for:


  • SIAM Journal on Scientific Computing

  • Partial Differential Equations and Applications

  • MathematicS in Action

  • Digital Finance

  • IMA Journal of Numerical Analysis