We present a parsimonious neural network approach, which does not rely on
dynamic programming techniques, to solve dynamic portfolio optimization
problems subject to multiple investment constraints. The number of parameters
of the (potentially deep) neural network remains independent of the number of
portfolio rebalancing events, and in contrast to, for example, reinforcement
learning, the approach avoids the computation of high-dimensional conditional
expectations. As a result, the approach remains practical even when considering
large numbers of underlying assets, long investment time horizons or very
frequent rebalancing events. We prove convergence of the numerical solution to
the theoretical optimal solution of a large class of problems under fairly
general conditions, and present ground truth analyses for a number of popular
formulations, including mean-variance and mean-conditional value-at-risk
problems. We also show that it is feasible to solve Sortino ratio-inspired
objectives (penalizing only the variance of wealth outcomes below the mean) in
dynamic trading settings with the proposed approach. Using numerical
experiments, we demonstrate that if the investment objective functional is
separable in the sense of dynamic programming, the correct time-consistent
optimal investment strategy is recovered, otherwise we obtain the correct
pre-commitment (time-inconsistent) investment strategy. The proposed approach
remains agnostic as to the underlying data generating assumptions, and results
are illustrated using (i) parametric models for underlying asset returns, (ii)
stationary block bootstrap resampling of empirical returns, and (iii)
generative adversarial network (GAN)-generated synthetic asset returns.