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

Abstract EN

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.