  This paper investigates the existence of a G-relaxed optimal control of a
controlled stochastic differential delay equation driven by G-Brownian motion
(G-SDDE in short). First, we show that optimal control of G-SDDE exists for the
finite horizon case. We present as an application of our result an economic
model, which is represented by a G-SDDE, where we studied the optimization of
this model. We connected the corresponding Hamilton Jacobi Bellman equation of
our controlled system to a decoupled G-forward backward stochastic differential
delay equation (G-FBSDDE in short). Finally, we simulate this G-FBSDDE to get
the optimal strategy and cost.
