Optimal control problems of forward-backward stochastic Volterra integralequations (FBSVIEs, in short) with closed control regions are formulated andstudied. Instead of using spike variation method as one may imagine, here weturn to treat the non-convexity of the control regions by borrowing some toolsin set-valued analysis and adapting them into our stochastic control systems. Aduality principle between linear backward stochastic Volterra integralequations and linear stochastic Fredholm-Volterra integral equations withconditional expectation are derived, which extends and improves thecorresponding results in [25], [30]. Some first order necessary optimalityconditions for optimal controls of FBSVIEs are established. In contrast withexisted common routines to treat the non-convexity of stochastic controlproblems, here only one adjoint system and one-order differentiabilityrequirements of the coefficients are needed.
展开▼
