Optimal control problems of forward-backwardstochastic Volterra integral equations Article Swipe

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Pontryagin's minimum principle Mathematics Volterra integral equation Fredholm integral equation Duality (order theory) Optimal control Integral equation Stochastic control Applied mathematics Maximum principle Type (biology) Field (mathematics) Mathematical analysis Mathematical optimization Pure mathematics Ecology Biology

Yufeng Shi , Tianxiao Wang , Jiongmin Yong ·

YOU? · · 2015 · Open Access · · DOI: https://doi.org/10.3934/mcrf.2015.5.613 · OA: W2519225972

Optimal control problems of forward-backward stochastic Volterraintegral equations (FBSVIEs, in short) are formulated and studied. Ageneral duality principle is established for linear backwardstochastic integral equation and linear stochastic Fredholm-Volterraintegral equation with mean-field. With the help of such a dualityprinciple, together with some other new delicate and subtle skills,Pontryagin type maximum principles are proved for two optimalcontrol problems of FBSVIEs.