CIRJE-F-993 | "Asymptotic Expansion for Forward-Backward SDEs with Jumps" |
Author Name | Fujii, Masaaki and Akihiko Takahashi |
Date | October 2015 |
Full Paper | PDF file |
Remarks | Revised as CIRJE-F-1094 (2018). |
Abstract |
The paper develops an asymptotic expansion method for forward-backward SDEs (FBSDEs) driven by the random Poisson measures with σ-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. |