We study deep learning-based schemes for solving high dimensional nonlinear
backward stochastic differential equations (BSDEs). First we show how to
improve the performances of the proposed scheme in [W. E and J. Han and A.
Jentzen, Commun. Math. Stat., 5 (2017), pp.349-380] regarding computational
time by using a single neural network architecture instead of the stacked deep
neural networks. Furthermore, those schemes can be stuck in poor local minima
or diverges, especially for a complex solution structure and longer terminal
time. To solve this problem, we investigate to reformulate the problem by
including local losses and exploit the Long Short Term Memory (LSTM) networks
which are a type of recurrent neural networks (RNN). Finally, in order to study
numerical convergence and thus illustrate the improved performances with the
proposed methods, we provide numerical results for several 100-dimensional
nonlinear BSDEs including nonlinear pricing problems in finance.Comment: 21 pages, 5 figures, 16 table