English

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

R2 v1 2026-06-21T17:58:24.884Z