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Optimal control problems of forward-backward stochastic Volterra integral equations

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  • Optimal control problems of forward-backward stochastic Volterra integral equations (FBSVIEs, in short) are formulated and studied. A general duality principle is established for linear backward stochastic integral equation and linear stochastic Fredholm-Volterra integral equation with mean-field. With the help of such a duality principle, together with some other new delicate and subtle skills, Pontryagin type maximum principles are proved for two optimal control problems of FBSVIEs.
    Mathematics Subject Classification: Primary: 60H20, 93E20; Secondary: 49K21, 49K45.

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