Optimal Control Problems of Forward-Backward Stochastic Volterra   Integral Equations
  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. 
Yufeng Shi, Tianxiao Wang and Jiongmin Yong
math.OC