Optimal control problems of forward-backward stochastic Volterra integral
equations (FBSVIEs in short) are formulated and studied. A general duality
principle is established for linear backward stochastic integral equation and
linear stochastic Fredholm-Volterra integral equation with mean-field. With the
help of such a duality principle, together with some other new delicate and
subtle skills, Pontryagin type maximum principles are proved for two optimal
control problems of FBSVIEs
