On an Asymptotic Expansion of Forward-Backward SDEs with a Perturbed Driver
ã€€ã€€ This paper presents a mathematical validity for an asymptotic expansion scheme of the solutions to the forwardbackward stochastic differential equations (FBSDEs) in terms of a perturbed driver in the BSDE and a small diffusion in the FSDE. This computational scheme was proposed by Fujii and Takahashi (2012a), which has been successfully employed to solve the derivatives and optimal portfolio problems in Fujii and Takahashi (2012b,c) and Fujii et al. (2012). In particular, we represent the coefficients up to an arbitrary order expansion of the BSDE by the solution to a system of the associated BSDEs with the FSDE, and obtain the error estimate of the expansion with respect to the driver perturbation. Accordingly, we show a concrete representation for each expansion coefficient of the volatility component, that is the martingale integrand in the BSDE. Then, we apply our proposed FSDE expansion formula with its precise error estimate to the BSDE expansion coefficients to finally obtain the total residual estimate.
|Date of creation:||Sep 2013|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.cirje.e.u-tokyo.ac.jp/index.html
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Masaaki Fujii & Seisho Sato & Akihiko Takahashi, 2012. "An FBSDE Approach to American Option Pricing with an Interacting Particle Method," Papers 1211.5867, arXiv.org.
- Masaaki Fujii & Akihiko Takahashi, 2012. "Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method," Papers 1204.2638, arXiv.org, revised Apr 2012.
- Masaaki Fujii & Akihiko Takahashi, 2012. "ANALYTICAL APPROXIMATION FOR NON-LINEAR FBSDEs WITH PERTURBATION SCHEME," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1250034-1-1.
When requesting a correction, please mention this item's handle: RePEc:tky:fseres:2013cf902. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CIRJE administrative office)
If references are entirely missing, you can add them using this form.