  We study the problem of optimal control of a coupled system of
forward-backward stochastic Volterra equations. We use Hida-Malliavin calculus
to prove a sufficient and a necessary maximum principle for the optimal control
of such systems. Existence and uniqueness of backward stochastic Volterra
integral equations are proved. As an application of our methods, we solve a
recursive utility optimisation problem in a financial model with memory.
