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Probability Theory and Related Fields

, Volume 142, Issue 1–2, pp 21–77 | Cite as

Well-posedness and regularity of backward stochastic Volterra integral equations

  • Jiongmin YongEmail author
Article

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.

Keywords

Backward stochastic Volterra integral equation Adapted M-solution Malliavin calculus Optimal control Pontryagin maximum principle 

Mathematics Subject Classification (2000)

60H20 60H07 93E20 49K22 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Central FloridaOrlandoUSA

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