# American Institute of Mathematical Sciences

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September  2015, 5(3): 613-649. doi: 10.3934/mcrf.2015.5.613

## Optimal control problems of forward-backward stochastic Volterra integral equations

 1 Institute for Financial Studies and School of Mathematics, Shandong University, Jinan, Shandong 250100 2 School of Mathematics, Sichuan University, Chengdu 610065, China 3 Department of Mathematics, University of Central Florida, Orlando, FL 32816

Received  April 2014 Revised  March 2015 Published  July 2015

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.
Citation: Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Optimal control problems of forward-backward stochastic Volterra integral equations. Mathematical Control & Related Fields, 2015, 5 (3) : 613-649. doi: 10.3934/mcrf.2015.5.613
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