The paper develops an asymptotic expansion method for forward-backward SDEs  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 before in a Brownian setup  . A 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, one can also handle a state-dependent intensity process, which is quite relevant for many practical applications  .
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 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 .
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(FBSDEs)
D
before
A
before
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one
the method
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a state-dependent intensity process, which is
sate-dependent (and hence non-Poissonian) jumps, which are
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. 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