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Solving forward-backward stochastic differential equations explicitly -- a four step scheme (1994)
| Content Provider | CiteSeerX |
|---|---|
| Author | Ma, Jin Protter, Philip Yong, Jiongmin |
| Abstract | In this paper we investigate the nature of the adapted solutions to a class of forward-backward stochastic differential equations (SDEs for short) in which the forward equation is non-degenerate. We prove that in this case the adapted solution can always be sought in an "ordinary" sense over an arbitrarily prescribed time duration, via a direct "Four Step Scheme". Using this scheme, we further prove that the backward components of the adapted solution are determined explicitly by the forward component via the solution of a certain quasi-linear parabolic PDE system. Moreover the uniqueness of the adapted solutions (over an arbitrary time duration), as well as the continuous dependence of the solutions on the parameters, can all be proved within this unified framework. Some special cases are studied separately. In particular, we derive a new form of the integral representation of the Clark-Haussmann-Ocone type for functionals (or functions) of diffusions, in which the conditional expectation is no longer needed. |
| File Format | |
| Journal | PROBAB. THEORY & RELAT. FIELDS |
| Language | English |
| Publisher Date | 1994-01-01 |
| Access Restriction | Open |
| Subject Keyword | Forward-backward Stochastic Differential Equation Step Scheme Adapted Solution Backward Component Direct Four Step Scheme Integral Representation Clark-haussmann-ocone Type Forward Component Certain Quasi-linear Parabolic Pde System Ordinary Sense Conditional Expectation Unified Framework Arbitrary Time Duration Continuous Dependence Special Case New Form Prescribed Time Duration Forward Equation |
| Content Type | Text |
| Resource Type | Article |
