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分類番号: CARF-F-372
発表時期: 2015 12
タイトル: Asymptotic Expansion for Forward-Backward SDEs with Jumps
著者: Masaaki Fujii, Akihiko Takahashi
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.

ファイル(PDF): full paper
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