Numerical probability

• Machine learning techniques

•  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,  2021, 59(1), 525-557. 

• 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.

• 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, 2020, vol 89(324), pp. 1547-1580

• 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. 

• 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 

• 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, https://doi.org/10.1007/s10915-022-01796-w  

• 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, 2023, Cambridge University Press, Editors: Agostino Capponi and Charles-Albert Lehalle, 

• Rate of convergence for particles approximation of PDEs in Wasserstein space (with M. Germain, X. Warin)

Journal of Applied Probability, 2022, vol 59(4), 992-1008

• Differential learning methods for solving fully nonlinear PDEs (with W. Lefebvre, G. Loeper)

Digital Finance, 2023, vol 5, 183-229,

• • Numerical methods and quantization