  We propose a deep neural network framework for computing prices and deltas of
American options in high dimensions. The architecture of the framework is a
sequence of neural networks, where each network learns the difference of the
price functions between adjacent timesteps. We introduce the least squares
residual of the associated backward stochastic differential equation as the
loss function. Our proposed framework yields prices and deltas on the entire
spacetime, not only at a given point. The computational cost of the proposed
approach is quadratic in dimension, which addresses the curse of dimensionality
issue that state-of-the-art approaches suffer. Our numerical simulations
demonstrate these contributions, and show that the proposed neural network
framework outperforms state-of-the-art approaches in high dimensions.
