| Abstract: |
We propose a machine learning algorithm for solving finite-horizon stochastic
control problems based on a deep neural network representation of the optimal
policy functions. The algorithm has three features: (1) It can solve
high-dimensional (e.g., over 100 dimensions) and finite-horizon
time-inhomogeneous stochastic control problems. (2) It has a monotonicity of
performance improvement in each iteration, leading to good convergence
properties. (3) It does not rely on the Bellman equation. To demonstrate the
efficiency of the algorithm, it is applied to solve various finite-horizon
time-inhomogeneous problems including recursive utility optimization under a
stochastic volatility model, a multi-sector stochastic growth, and optimal
control under a dynamic stochastic integration of climate and economy model
with eight-dimensional state vectors and 600 time periods. |