  We propose a novel data-driven neural network (NN) optimization framework for
solving an optimal stochastic control problem under stochastic constraints.
Customized activation functions for the output layers of the NN are applied,
which permits training via standard unconstrained optimization. The optimal
solution yields a multi-period asset allocation and decumulation strategy for a
holder of a defined contribution (DC) pension plan. The objective function of
the optimal control problem is based on expected wealth withdrawn (EW) and
expected shortfall (ES) that directly targets left-tail risk. The stochastic
bound constraints enforce a guaranteed minimum withdrawal each year. We
demonstrate that the data-driven approach is capable of learning a near-optimal
solution by benchmarking it against the numerical results from a
Hamilton-Jacobi-Bellman (HJB) Partial Differential Equation (PDE) computational
framework.
