Asymptotic Expansion for Forward-Backward SDEs with Jumps
39 Pages Posted: 13 Oct 2015 Last revised: 16 Sep 2018
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: Suggested Citation