Discussion Papers 2018
CIRJE-F-1094 | "Asymptotic Expansion for Forward-Backward SDEs with Jumps" |
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Author Name | Fujii, Masaaki and Akihiko Takahashi |
Date | September 2018 |
Full Paper | |
Remarks | Revised version of CIRJE-F-993(2015) forthcoming in Stochastics. |
Abstract |
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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. |