Asymptotic expansions as control variates for deep solvers to fully-coupled forward-backward stochastic differential equations

Makoto Naito, Taiga Saito, Akihiko Takahashi and Kohta Takehara

PLOS ONE, 2025, vol. 20, issue 5, 1-17

Abstract: Coupled forward-backward stochastic differential equations (FBSDEs) are closely related to financially important issues such as optimal investment. However, it is well known that obtaining solutions is challenging, even when employing numerical methods. In this paper, we propose new methods that combine an algorithm recently developed for coupled FBSDEs and an asymptotic expansion approach to those FBSDEs as control variates for learning of the neural networks. The proposed method is demonstrated to perform better than the original algorithm in numerical examples, including one with a financial implication. The results show that the proposed method exhibits not only faster convergence but also greater stability in computation.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0321778 (text/html)
https://journals.plos.org/plosone/article/file?id= ... 21778&type=printable (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0321778

DOI: 10.1371/journal.pone.0321778

Access Statistics for this article

More articles in PLOS ONE from Public Library of Science
Bibliographic data for series maintained by plosone ().