||"Asymptotic Expansion for Forward-Backward SDEs|
||Fuji, Masaaki and Akihiko Takahashi|
Revised version of CIRJE-F-993(2015) forthcoming in Stochastics.
This work provides a semi-analytic approximation method for decoupled forwardbackward
SDEs (FBSDEs) with jumps. In particular, we construct an asymptotic
expansion method for FBSDEs driven by the random Poisson measures with σ-finite
compensators as well as the standard Brownian motions around the small-variance
limit of the forward SDE. We provide a semi-analytic solution technique as well as its
error estimate for which we only need to solve essentially a system of linear ODEs.
In the case of a finite jump measure with a bounded intensity, the method can also
handle state-dependent and hence non-Poissonian jumps, which are quite relevant for
many practical applications.