Mean-field backward stochastic Volterra integral equations

Yufeng Shi; Tianxiao Wang; Jiongmin Yong

doi:10.3934/dcdsb.2013.18.1929

Article Contents

2013, Volume 18, Issue 7: 1929-1967. Doi: 10.3934/dcdsb.2013.18.1929

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Mean-field backward stochastic Volterra integral equations

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

Received: August 31, 2012

Revised: February 28, 2013

Published: August 2013

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Abstract

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

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Mathematics Subject Classification: 60H20, 93E20, 35Q83.

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