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-Takahashi (2012a), which has been successfully employed to solve the derivatives and optimal portfolio problems in Fujii-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.
内容記述
本文フィルはリンク先を参照のこと
雑誌名
Discussion paper series. CIRJE-F
巻
CIRJE-F-902
発行年
2013-09
書誌レコードID
AA11450569
フォーマット
application/pdf
出版者
日本経済国際共同センター
出版者別名
Center for International Research on the Japanese Economy
On an Asymptotic Expansion of Forward-Backward SDEs with a Perturbed Driver
