by Côme Huré, Huyên Pham, Achref Bachouch & Nicolas Langrené
This paper presents several numerical applications of deep learning-based algorithms that have been analyzed in [Bachouch et al., 2018a]. Numerical and comparative tests using TensorFlow illustrate the performance of our different algorithms, namely control learning by performance iteration (algorithms NNcontPI and ClassifPI), control learning by hybrid iteration (algorithms Hybrid-Now and Hybrid-LaterQ), on the 100-dimensional nonlinear PDEs examples from [Weinan et al. 2017] and on quadratic Backward Stochastic Differential equations as in [Chassagneux et al., 2016]. We also provide numerical results for an option hedging problem in finance, and energy storage problems arising in the valuation of gas storage and in microgrid management.