An Optimal Control Problem of Forward-Backward Stochastic Volterra Integral Equations with State Constraints
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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.
1989 ◽
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