An Asymptotic Expansion of Forward-Backward SDEs with a Perturbed Driver (Forthcoming in International Journal of Financial Engineering”)”

Abstract

Inspired by non-linear pricing in finance, this paper presents a mathematical validity of an
asymptotic expansion scheme for a system of forward-backward stochastic differential equations (FBSDEs) in terms of a perturbed driver in the BSDE and a small diffusion in the FSDE. In particular, we represent the coefficients of the expansion of the FBSDE up to an arbitrary order, and obtain the error estimate of the expansion with respect to the driver and the small noise perturbation.