 Asymptotic Expansion for Forward-Backward SDEsMasaaki Fujii and
Akihiko Takahashi
No CARF-F-372, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo Abstract: The paper develops an asymptotic expansion method for forward-backward SDEs (FBSDEs) driven by the random Poisson measures with σ-finite compensators. The expansion is performed around the small-variance limit of the forward SDE and does not necessarily require a small size of the non-linearity in the BSDE’s driver, which was actually the case for the linearization method proposed by the current authors in a Brownian setup before. A semi-analytic solution technique, which only requires a system of ODEs (one is non-linear and the others are linear) to be solved, as well as its error estimate are provided. In the case of a finite jump measure with a bounded intensity, the method can also handle sate-dependent (and hence non-Poissonian) jumps, which are quite relevant for many practical applications. Based on the stability result, we also provide a rigorous justification to use arbitrarily smooth coefficients in FBSDEs for any approximation purpose whenever rather mild conditions are satisfied. Pages: 39 pages Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:cfi:fseres:cf372 Access Statistics for this paper More papers in CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo Contact information at EDIRC. |
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