Linear Forward-Backward Stochastic Differential Equations
- 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, Vol. 39, Issue 1; Other Information: DOI: 10.1007/s002459900100; Copyright (c) 1999 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 1999 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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