Mean-Field Backward Stochastic Volterra Integral Equations
Probability
2011-07-06 v2 Systems and Control
Optimization and Control
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. As applications, a multi-dimensional comparison theorem is proved for adapted M-solutions of MF-BSVIEs and a maximum principle is established for an optimal control of MF-FSVIEs.
Keywords
Cite
@article{arxiv.1104.4725,
title = {Mean-Field Backward Stochastic Volterra Integral Equations},
author = {Yufeng Shi and Tianxiao Wang and Jiongmin Yong},
journal= {arXiv preprint arXiv:1104.4725},
year = {2011}
}
Comments
54 pages