Linear forward-backward stochastic differential equations with random coefficients

    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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