Linear-Quadratic Stochastic Delayed Control and Deep Learning Resolution

We consider a simple class of stochastic control problems with delayed control, in both the drift and diffusion part state differential equation. provide new characterization solution terms set Riccati partial equations. Existence uniqueness are obtained under sufficient condition expressed directly as relation between time horizon, drift, volatility delay. Furthermore, deep learning scheme (The code is available IPython notebook.) designed used to illustrate effect delay feature on Markowitz portfolio allocation problem execution