Title

Linear forward-backward stochastic differential equations with random coefficients

Authors

Authors

J. M. Yong

Comments

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Abbreviated Journal Title

Probab. Theory Relat. Field

Keywords

linear forward-backward stochastic differential equation; adapted; solution; decoupling reduction; Riccati backward stochastic differential; equation; CONTROL WEIGHT COSTS; RICCATI-EQUATIONS; QUADRATIC REGULATORS; CONSTRAINTS; Statistics & Probability

Abstract

Solvability of linear forward-backward stochastic differential equations (FBSDEs, for short) with random coefficients is studied. A decoupling reduction method is introduced via which a large class of linear FBSDEs with random or deterministic time-varying coefficients is proved to be solvable. On the other hand, by means of Four Step Scheme, a Riccati backward stochastic equation (BSDE, for short) for (mxn) matrix-valued processes is derived. Global solvability of such Riccati BSDEs is discussed for some special (but nontrivial) cases, which leads to the solvability of the corresponding linear FBSDEs.

Journal Title

Probability Theory and Related Fields

Volume

135

Issue/Number

1

Publication Date

1-1-2006

Document Type

Article

Language

English

First Page

53

Last Page

83

WOS Identifier

WOS:000235447900003

ISSN

0178-8051

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