Mean-Field Backward Stochastic Volterra Integral Equations

Details Mean-Field Backward Stochastic Volterra Integral Equations Mean-Field Backward Stochastic Volterra Integral Equations

2011-04-25

arxiv.org/abs/1104.4725v2

Mathematics

Probability

54 pages

Scientific paper

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.

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