scholarly journals Asymptotic expansion for forward-backward SDEs with jumps

Stochastics ◽  
2018 ◽  
Vol 91 (2) ◽  
pp. 175-214 ◽  
Author(s):  
Masaaki Fujii ◽  
Akihiko Takahashi
Keyword(s):  
Asymptotic Expansion ◽  
Backward Sdes

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

2015 ◽  
Vol 02 (02) ◽  
pp. 1550020 ◽  
Author(s):  
Akihiko Takahashi ◽  
Toshihiro Yamada
Keyword(s):  
Asymptotic Expansion ◽  
Differential Equations ◽  
Error Estimate ◽  
Arbitrary Order ◽  
Nonlinear Pricing ◽  
Small Noise ◽  
Small Diffusion ◽  
Noise Perturbation ◽  
Backward Sdes ◽  
Expansion Scheme

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.

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