Asymptotic Expansion for Forward-Backward SDEs with JumpsAsymptotic Expansion for Forward-Backward SDEs with Jumps (Forthcoming in Stochastics) (Revised version of F-372)

Masaaki Fujii and Akihiko Takahashi
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Masaaki Fujii: Quantitative Finance Course, Graduate School of Economics, The University of Tokyo
Akihiko Takahashi: Quantitative Finance Course, Graduate School of Economics, The University of Tokyo

No CARF-F-445, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: This work provides a semi-analytic approximation method for decoupled forward- backward 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 ï¬ nite 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.

Pages: 40
Date: 2018-09
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