An asymptotic expansion of forward-backward SDEs with a perturbed driver

Akihiko Takahashi and Toshihiro Yamada ()
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Akihiko Takahashi: University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo, Japan
Toshihiro Yamada: University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo, Japan;

International Journal of Financial Engineering (IJFE), 2015, vol. 02, issue 02, 1-29

Abstract: Motivated by nonlinear 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.

Keywords: Forward-backward SDEs; asymptotic expansion; nonlinear pricing; Malliavin calculus (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (22)

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DOI: 10.1142/S2424786315500206

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