 Explicit solution to delayed forward and backward stochastic differential equationsTianfu Ma, Juanjuan Xu and Huanshui Zhang International Journal of Systems Science, 2024, vol. 55, issue 10, 2144-2153 Abstract: This paper is concerned with the linear delayed forward–backward stochastic differential equations (D-FBSDEs). The existence of time delay leads to the infinite-dimensional problem which makes the explicit solvability more challenging. The main contribution is to propose a discretisation approach which gives the explicit solution of the D-FBSDEs and consists of the following three steps: first, we transform the continuous-time D-FBSDEs into the discrete-time form with the aid of interval partition. Second, we derive the solution of the discrete-time D-FBSDEs by applying backward iterative induction. Finally the explicit solution of the continuous-time D-FBSDEs is obtained by taking the limit to the solution of discrete-time form which is also strictly proved under continuous-time framework. The proposed approach is applicable for more general FBSDEs with delay, which would provide a complete solution to the stochastic LQ control with time delay. Date: 2024 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:tsysxx:v:55:y:2024:i:10:p:2144-2153 Ordering information: This journal article can be ordered from DOI: 10.1080/00207721.2024.2335218 Access Statistics for this article International Journal of Systems Science is currently edited by Visakan Kadirkamanathan More articles in International Journal of Systems Science from Taylor & Francis Journals |
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