Title

Linear Forward-Backward Stochastic Differential Equations With Random Coefficients

Keywords

Adapted solution; Decoupling reduction; Linear forward-backward stochastic differential equation; Riccati backward stochastic differential equation

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 (m×n) 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.

Publication Date

5-1-2006

Publication Title

Probability Theory and Related Fields

Volume

135

Issue

1

Number of Pages

53-83

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00440-005-0452-5

Socpus ID

32944478196 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/32944478196

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