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Linear Forward-Backward Stochastic Differential Equations

Journal Article · · Applied Mathematics and Optimization
DOI:https://doi.org/10.1007/S002459900100· OSTI ID:21064289
 [1]
  1. Department of Mathematics, Fudan University, Shanghai 200433 (China)
The problem of finding adapted solutions to systems of coupled linear forward-backward stochastic differential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability in control theory, using some functional analysis, we obtain a necessary and sufficient condition for the solvability of a class of linear FBSDEs. Then a Riccati-type equation for matrix-valued (not necessarily square) functions is derived using the idea of the Four-Step Scheme (introduced in [11] for general FBSDEs). The solvability of such a Riccati-type equation is studied which leads to a representation of adapted solutions to linear FBSDEs.
OSTI ID:
21064289
Journal Information:
Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 1 Vol. 39; ISSN 0095-4616
Country of Publication:
United States
Language:
English

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