Mean-field backward stochastic Volterra integral equations

Yufeng Shi; Tianxiao Wang; Jiongmin Yong

doi:10.3934/dcdsb.2013.18.1929

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Mean-field backward stochastic Volterra integral equations

Yufeng Shi Tianxiao Wang Jiongmin Yong

Year: 2013 Journal: Discrete and Continuous Dynamical Systems - B Vol: 18 (7)Pages: 1929-1967 Publisher: American Institute of Mathematical Sciences

DOI: 10.3934/dcdsb.2013.18.1929

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Abstract

Mean-field backward stochastic Volterra integral equations(MF-BSVIEs, for short) are introduced and studied. Well-posedness ofMF-BSVIEs in the sense of introduced adapted M-solutions isestablished. Two duality principles between linear mean-field(forward) stochastic Volterra integral equations (MF-FSVIEs, forshort) and MF-BSVIEs are obtained. A Pontryagin's type maximumprinciple is established for an optimal control of MF-FSVIEs.

Keywords:

Volterra integral equation Mathematics Pontryagin's minimum principle Duality (order theory) Integral equation Field (mathematics) Applied mathematics Type (biology) Volterra equations Mathematical analysis Stratonovich integral Optimal control Mathematical optimization Pure mathematics Nonlinear system Physics Singular integral Riemann integral

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Stochastic processes and financial applications

Social Sciences → Economics, Econometrics and Finance → Finance

Nonlinear Differential Equations Analysis

Physical Sciences → Mathematics → Applied Mathematics

Stability and Controllability of Differential Equations

Physical Sciences → Engineering → Control and Systems Engineering

Mean-field backward stochastic Volterra integral equations

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