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Backward Stochastic Differential Equations with No Driving Martingale, Markov Processes and Associated Pseudo-Partial Differential Equations: Part II—Decoupled Mild Solutions and Examples. J THEOR PROBAB 2021. [DOI: 10.1007/s10959-021-01092-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Backward stochastic dynamics with a subdifferential operator and non-local parabolic variational inequalities. Stoch Process Their Appl 2018. [DOI: 10.1016/j.spa.2017.06.005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Casserini M, Liang G. Fully coupled forward–backward stochastic dynamics and functional differential systems. STOCH DYNAM 2015. [DOI: 10.1142/s0219493715500069] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This paper introduces and solves a general class of fully coupled forward–backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different types of forward–backward stochastic differential equations (FBSDEs) that do not fit in the classical setting. In our approach, the equations are running in the same time direction rather than in a forward and backward way, and the conflicting nature of the structure of FBSDEs is therefore avoided.
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Affiliation(s)
| | - Gechun Liang
- Department of Mathematics, King's College London, UK
- Oxford-Man Institute, University of Oxford, UK
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