Machine learning
Neural networks methods and algorithms for stochastic control and PDEs
Mean-field neural networks: learning mappings on Wasserstein space, (with X. Warin)
To appear in Neural Networks, [ResearchGate], [arXiv:2210.15179]
Mean-field neural networks-based algorithms for McKean-Vlasov control problems (with X. Warin)
Submitted, [ResearchGate], [arXiv:2212.11518]
Differential learning methods for solving fully nonlinear PDEs (with W. Lefebvre, G. Loeper)
Digital Finance, 2023, vol 5, 183-229, [Researchgate],[arXiv:2205:09815]
DeepSets and their derivative networks for solving symmetric PDEs (with M. Germain, M. Laurière, X. Warin)
Journal of Scientific Computing, 2022, Vol 91, article 63, [Researchgate], [arXiv:2103.00838]
Neural networks-based algorithms for stochastic control and PDEs in finance (with M. Germain, X. Warin)
Machine Learning for Financial Markets: a guide to contemporary practices, Cambridge University Press, Editors: Agostino Capponi and Charles-Albert Lehalle, [arXiv:2101.08068]
Discrete-time portfolio optimization under maximum drawdown constraint with partial information and deep learning resolution (with C. De Franco, J. Nicolle)
Stochastic Analysis, Filtering, and Stochastic Optimizations: A Commemorative Volume to Honor Mark H. A. Davis's Contributions, eds. G. Yin, T. Zariphopoulou, [arXiv:2010.15779]
Approximation error analysis of some deep backward schemes for nonlinear PDEs (with M. Germain, X. Warin)
SIAM Journal of Scientific Computing, 2022, Vol 44(1), A28-A56, [arXiv:2006.01496]
Neural networks-based backward scheme for fully nonlinear PDEs (with M. Germain, X. Warin)
SN Partial Differential Equations and Applications, 2021, Vol 2(1), article 16, [Researchgate]
Deep backward schemes for high-dimensional nonlinear PDEs (formerly entitled: Some machine learning schemes for high-dimensional nonlinear PDEs)
(with C. Huré, X. Warin)
Mathematics of Computation, 89(324), 1547-1580
Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysis (with C. Huré, A. Bachouch, N. Langrené)
SIAM Journal on Numerical Analysis, 59(1), 525-557, [arXiv:1812.04300]
Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications (with A. Bachouch, C. Huré, N. Langrené)
Methodology and Computing in Applied Probability, 2022, Vol 24, pp 143-178, https://doi.org/10.1007/s11009-019-09767-9, [arXiv:1812.05916]
Reinforcement learning
Actor critic learning algorithms for mean field control with moment neural networks (with X. Warin)
Submitted, [arXiv:2309.04317]
Actor-critic learning for mean-field control in continuous time (with N. Frikha, M. Germain, M. Laurière, and X. Song)
Submitted, [ResearchGate], [arXiv:2303.06993]
Policy gradient learning methods for stochastic control with exit time and applications to share repurchase pricing (with M. Hamdouche and P. Henry Labordère)
Applied Mathematical Finance, 2023, 29(6), 439-456,
Generative modeling
Generative modeling for time series via Schrödinger bridge (with M. Hamdouche and P. Henry-Labordère)
submitted, [ResearchGate], [arXiv:2304.05093]
Codes and Jupyter Notebooks