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

Relaxed Optimal Control Problem for a Finite Horizon G-SDE with Delay and Its Application in Economics