M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen et al., TensorFlow: Large-scale machine learning on heterogeneous systems, 2015.

F. Albertini and E. D. Sontag, Uniqueness of weights for recurrent nets, MATHEMATICAL RESEARCH, vol.79, pp.599-599, 1994.

F. Albertini, E. D. Sontag, and V. Maillot, Uniqueness of weights for neural networks. Artificial Neural Networks for Speech and Vision, pp.115-125, 1993.

L. Andersen and M. Broadie, Primal-dual simulation algorithm for pricing multidimensional american options, Management Science, vol.50, issue.9, pp.1222-1234, 2004.

V. I. Arnold, On functions of three variables, Collected Works: Representations of Functions, Celestial Mechanics and KAM Theory, pp.5-8, 1957.

V. Bally and G. Pages, A quantization algorithm for solving multidimensional discrete-time optimal stopping problems, Bernoulli, vol.9, issue.6, pp.1003-1049, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00104798

S. Becker, P. Cheridito, and A. Jentzen, Deep optimal stopping, Journal of Machine Learning Research, vol.20, issue.74, pp.1-25, 2019.

S. Becker, P. Cheridito, A. Jentzen, and T. Welti, Solving high-dimensional optimal stopping problems using deep learning, 2019.

B. Bouchard and X. Warin, Monte-carlo valuation of american options: Facts and new algorithms to improve existing methods, Numerical Methods in Finance, vol.12, pp.215-255, 2012.

M. Broadie and P. Glasserman, A stochastic mesh method for pricing high-dimensional american options, Journal of Computational Finance, vol.7, pp.35-72, 2004.

A. L. Bronstein, G. Pagès, and J. Portès, Multi-asset american options and parallel quantization, Methodology and Computing in Applied Probability, vol.15, issue.3, pp.547-561, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00320199

J. F. Carriere, Valuation of the early-exercise price for options using simulations and nonparametric regression, Insurance: mathematics and Economics, vol.19, issue.1, pp.19-30, 1996.

E. Clément, D. Lamberton, and P. Protter, An analysis of a least squares regression method for american option pricing, Finance and Stochastics, vol.6, issue.4, pp.449-471, 2002.

J. Cox, S. Ross, and M. Rubinstein, Option pricing: A simplified approach, Journal of Financial Economics, issue.7, pp.229-263, 1979.

G. Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of Control, Signals and Systems, vol.2, issue.4, pp.303-314, 1989.

F. Fang and C. W. Oosterlee, Pricing early-exercise and discrete barrier options by fourier-cosine series expansions, Numerische Mathematik, vol.114, issue.1, p.27, 2009.

P. Glasserman and B. Yu, Number of paths versus number of basis functions in american option pricing, The Annals of Applied Probability, vol.14, issue.4, pp.2090-2119, 2004.

E. Gobet, J. Lemor, and X. Warin, A regression-based Monte Carlo method to solve backward stochastic differential equations, Annals of Applied Probability, vol.15, issue.3, pp.2172-2202, 2005.

K. Hornik, Approximation capabilities of multilayer feedforward networks, Neural Networks, vol.4, issue.2, pp.251-257, 1991.

M. Kohler, A. Krzy?ak, and N. Todorovic, Pricing of high-dimensional american options by neural networks, Mathematical Finance: An International Journal of Mathematics, Statistics and Financial Economics, vol.20, issue.3, pp.383-410, 2010.

A. Kolmogorov, On the representation of continuous functions of several variables as superpositions of functions of smaller number of variables, In Soviet. Math. Dokl, vol.108, pp.179-182, 1956.

M. Ledoux and M. Talagrand, Probability in Banach spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol.23, issue.3

. Springer-verlag, , 1991.

F. Longstaff and R. Schwartz, Valuing American options by simulation : A simple least-square approach, Review of Financial Studies, vol.14, pp.113-147, 2001.

R. Lord, F. Fang, F. Bervoets, and C. W. Oosterlee, A fast and accurate fft-based method for pricing early-exercise options under lévy processes, SIAM Journal on Scientific Computing, vol.30, issue.4, pp.1678-1705, 2008.

G. Pagès, Numerical Probability: An Introduction with Applications to Finance, 2018.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion et al., Scikit-learn: Machine Learning in Python, Journal of Machine Learning Research, vol.12, pp.2825-2830, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00650905

A. Pinkus, Approximation theory of the mlp model in neural networks, Acta numerica, vol.8, pp.143-195, 1999.

R. Y. Rubinstein and A. Shapiro, Sensitivity analysis and stochastic optimization by the score function method, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics

J. A. Tilley, Valuing american options in a path simulation model, Transactions of the Society of Actuaries, vol.45, issue.83, p.104, 1993.

J. Tsitsiklis and B. V. Roy, Regression methods for pricing complex American-style options, IEEE Trans. Neural Netw, vol.12, issue.4, pp.694-703, 2001.

R. C. Williamson and U. Helmke, Existence and uniqueness results for neural network approximations, IEEE Transactions on Neural Networks, vol.6, issue.1, pp.2-13, 1995.