Articlediamond2015

Optimal control problems of forward-backward stochastic Volterra integral equations

Yufeng Shi · Tianxiao Wang · Jiongmin Yong

39 citations0/0 files storedMathematical Control and Related Fields

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Fuzzy Systems and Optimization

Abstract

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.

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References

2007Brownian Motion and Stochastic Calculus 1999Stochastic controls : Hamiltonian systems and HJB equations 1999Stochastic Controls 1992Stochastic Differential Utility 1992Picoeconomics: The Strategic Interaction of Successive Motivational States within the Person 1990A General Stochastic Maximum Principle for Optimal Control Problems 2007Forward-Backward Stochastic Differential Equations and their Applications 1993Backward stochastic differential equations and applications to optimal control

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2019Recursive Utility Processes, Dynamic Risk Measures and Quadratic Backward Stochastic Volterra Integral Equations 2021Time-inconsistent stochastic optimal control problems and backward stochastic volterra integral equations 2020Backward doubly stochastic Volterra integral equations and their applications 2017Linear quadratic control problems of stochastic Volterra integral equations 2020Extended backward stochastic Volterra integral equations, Quasilinear parabolic equations, and Feynman–Kac formula

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