The paper develops an asymptotic expansion method for forward-backward SDEs (FBSDEs)  driven by the random Poisson measures with sigma-finite compensators . The expansion is performed  around the small-variance limit of the forward SDE and does not necessarily require a small size of the non-linearity in the BSDE's driver, which was actually the case for the linearization method proposed by the current authors in a Brownian setup before. A semi-analytic solution technique , which only requires a system of ODEs (one is non-linear and the others are linear) to be solved, as well as its error estimate are provided . In the case of a finite jump measure with a bounded intensity, the method can also handle sate-dependent ( and hence non-Poissonian ) jumps, which are quite relevant for many practical applications . Based on the stability result, we also provide a rigorous justification to use arbitrarily smooth coefficients in FBSDEs for any approximation purpose whenever rather mild conditions are satisfied .
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 \sigma -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 .
R
The paper develops an asymptotic expansion method for forward-backward
This work provides a semi-analytic approximation method for decoupled forwardbackward
A
with jumps. In particular, we construct an asymptotic expansion method for FBSDEs
R
sigma-finite compensators . The expansion is performed
\sigma
A
-finite compensators as well as the standard Brownian motions
R
and does not necessarily require a small size of the non-linearity in the BSDE's driver, which was actually the case for the linearization method proposed by the current authors in a Brownian setup before. A
. We provide a
D
, which only requires a system of ODEs (one is non-linear and the others are linear) to be solved,
R
are provided
for which we only need to solve essentially a system of linear ODEs
R
sate-dependent (
state-dependent
D
)
D
. Based on the stability result, we also provide a rigorous justification to use arbitrarily smooth coefficients in FBSDEs for any approximation purpose whenever rather mild conditions are satisfied