  Many real world stochastic control problems suffer from the "curse of
dimensionality". To overcome this difficulty, we develop a deep learning
approach that directly solves high-dimensional stochastic control problems
based on Monte-Carlo sampling. We approximate the time-dependent controls as
feedforward neural networks and stack these networks together through model
dynamics. The objective function for the control problem plays the role of the
loss function for the deep neural network. We test this approach using examples
from the areas of optimal trading and energy storage. Our results suggest that
the algorithm presented here achieves satisfactory accuracy and at the same
time, can handle rather high dimensional problems.
