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 inequalities. Then, by dual method, we derive a stochastic maximum principle which gives the necessary conditions for the optimal controls.
"An Optimal Control Problem of Forward-Backward Stochastic Volterra Integral Equations with State Constraints." Abstr. Appl. Anal. 2014 (SI35) 1 - 16, 2014. https://doi.org/10.1155/2014/432718