  We consider a class of stochastic control problems with a delayed control,
both in drift and diffusion, of the type dX t = $\alpha$ t--d (bdt + $\sigma$dW
t). We provide a new characterization of the solution in terms of a set of
Riccati partial differential equations. Existence and uniqueness are obtained
under a sufficient condition expressed directly as a relation between the
horizon T and the quantity d(b/$\sigma$) 2. Furthermore, a deep learning scheme
is designed and used to illustrate the effect of delay on the Markowitz
portfolio allocation problem with execution delay.
