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

Masaaki Fujii and Akihiko Takahashi
Additional contact information
Masaaki Fujii: Graduate School of Economics, The University of Tokyo
Akihiko Takahashi: Graduate School of Economics, University of Tokyo

No CARF-F-278, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

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.

Pages: 22 pages
Date: 2012-04, Revised 2015-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (23)

Downloads: (external link)
https://www.carf.e.u-tokyo.ac.jp/old/pdf/workingpaper/fseries/F278.pdf (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:cfi:fseres:cf278

Access Statistics for this paper

More papers in CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo Contact information at EDIRC.
Bibliographic data for series maintained by ().