Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method

Masaaki Fujii () and Akihiko Takahashi ()

Asia-Pacific Financial Markets, 2015, vol. 22, issue 3, 283-304

Abstract: In this paper, we propose an efficient Monte Carlo implementation of a non-linear FBSDE as a system of interacting particles inspired by the idea of the branching diffusion method of McKean. It will be particularly useful to investigate large and complex systems, and hence it is a good complement of our previous work presenting an analytical perturbation procedure for generic non-linear FBSDEs. There appear multiple species of particles, where the first one follows the diffusion of the original underlying state, and the others the Malliavin derivatives with a grading structure. The number of branching points are capped by the order of perturbation, which is expected to make the scheme less numerically intensive. The proposed method can be applied to semi-linear problems, such as American options, credit and funding value adjustments, and even fully non-linear issues, such as the optimal portfolio problems in incomplete and/or constrained markets. Copyright Springer Japan 2015

Keywords: BSDE; FBSDE; Asymptotic expansion; Malliavin derivative; Interacting particle method; Branching diffusion (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (21)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10690-015-9201-7 (text/html)
Access to full text is restricted to subscribers.

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:kap:apfinm:v:22:y:2015:i:3:p:283-304

Ordering information: This journal article can be ordered from
http://www.springer.com/finance/journal/10690/PS2

DOI: 10.1007/s10690-015-9201-7

Access Statistics for this article

Asia-Pacific Financial Markets is currently edited by Jiro Akahori

More articles in Asia-Pacific Financial Markets from Springer, Japanese Association of Financial Economics and Engineering
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().