Perturbative Expansion Technique for Non-Linear FBSDEs With Interacting Particle Method

21 Pages Posted: 13 Apr 2012 Last revised: 1 Dec 2014

See all articles by Masaaki Fujii

Masaaki Fujii

University of Tokyo - Faculty of Economics

Akihiko Takahashi

University of Tokyo - Faculty of Economics

Date Written: November 28, 2014

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.

Keywords: BSDE, FBSDE, interacting particle method, branching diffusion, Malliavin derivative, asymptotic expansion

JEL Classification: C15, C61, G10, G11, G12, G13

Suggested Citation

Fujii, Masaaki and Takahashi, Akihiko, Perturbative Expansion Technique for Non-Linear FBSDEs With Interacting Particle Method (November 28, 2014). Available at SSRN: https://ssrn.com/abstract=2038740 or http://dx.doi.org/10.2139/ssrn.2038740

Masaaki Fujii (Contact Author)

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

Akihiko Takahashi

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

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