Asymptotic Expansion for Forward-Backward SDEs with Jumps

39 Pages Posted: 13 Oct 2015 Last revised: 16 Sep 2018

See all articles by Masaaki Fujii

Masaaki Fujii

University of Tokyo - Faculty of Economics

Akihiko Takahashi

University of Tokyo - Faculty of Economics

Date Written: September 7, 2018

Abstract

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.

Keywords: SDE, jumps, random measure, asymptotic expansion, Levy process

JEL Classification: C00, G12, G13

Suggested Citation

Fujii, Masaaki and Takahashi, Akihiko, Asymptotic Expansion for Forward-Backward SDEs with Jumps (September 7, 2018). Available at SSRN: https://ssrn.com/abstract=2672890 or http://dx.doi.org/10.2139/ssrn.2672890

Masaaki Fujii (Contact Author)

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

Akihiko Takahashi

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
102
Abstract Views
860
Rank
473,049
PlumX Metrics