Abstract
Backward stochastic Volterra integral equations (BSVIEs, for short) are studied. Notion of adapted M-solution is introduced. Well-posedness of BSVIEs is established and some regularity results are proved for the adapted M-solutions via Malliavin calculus. A Pontryagin type maximum principle is presented for optimal controls of stochastic Volterra integral equations.
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This work is supported in part by NSF Grant DMS-0604309.
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Yong, J. Well-posedness and regularity of backward stochastic Volterra integral equations. Probab. Theory Relat. Fields 142, 21–77 (2008). https://doi.org/10.1007/s00440-007-0098-6
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DOI: https://doi.org/10.1007/s00440-007-0098-6
Keywords
- Backward stochastic Volterra integral equation
- Adapted M-solution
- Malliavin calculus
- Optimal control
- Pontryagin maximum principle