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Title: Linear Forward-Backward Stochastic Differential Equations

Abstract

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.

Authors:
 [1]
  1. Department of Mathematics, Fudan University, Shanghai 200433 (China)
Publication Date:
OSTI Identifier:
21064289
Resource Type:
Journal Article
Journal Name:
Applied Mathematics and Optimization
Additional Journal Information:
Journal Volume: 39; Journal 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); Journal ID: ISSN 0095-4616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONTROL THEORY; DIFFERENTIAL EQUATIONS; FUNCTIONAL ANALYSIS; FUNCTIONS; MATHEMATICAL SOLUTIONS; MATRICES; STOCHASTIC PROCESSES

Citation Formats

Yong Jiongmin. Linear Forward-Backward Stochastic Differential Equations. United States: N. p., 1999. Web. doi:10.1007/S002459900100.
Yong Jiongmin. Linear Forward-Backward Stochastic Differential Equations. United States. doi:10.1007/S002459900100.
Yong Jiongmin. Fri . "Linear Forward-Backward Stochastic Differential Equations". United States. doi:10.1007/S002459900100.
@article{osti_21064289,
title = {Linear Forward-Backward Stochastic Differential Equations},
author = {Yong Jiongmin},
abstractNote = {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.},
doi = {10.1007/S002459900100},
journal = {Applied Mathematics and Optimization},
issn = {0095-4616},
number = 1,
volume = 39,
place = {United States},
year = {1999},
month = {1}
}