Work

Asymptotic expansion for forward-backward SDEs with jumps

Year: 2018

Type: article

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 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.

Source: Stochastics

DOI: 10.1080/17442508.2018.1521808

Authors: Masaaki Fujii, Akihiko Takahashi

Institution: The University of Tokyo

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: Cicatricial Alopecia Research Foundation, Japan Society for the Promotion of Science

Award: Research on Derivatives Pricing and Risk Management after Financial Crisis