An optimal control problem of forward-backward stochastic Volterra   integral equations with state constraints
  This paper is devoted to the stochastic optimal control problems for systems governed by forward-backward stochastic Volterra integral equations (FBSVIEs, for short) with state constraints. Using Ekeland's variational principle, we obtain one kind of variational inequality. Then, by dual method, we derive a stochastic maximum principle which gives the necessary conditions for the optimal controls. 
Qingmeng Wei, Xinling Xiao
math-ph math.MP math.OC