英文标题：
《Asymptotic Expansion for Forward-Backward SDEs with Jumps》
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作者：
Masaaki Fujii and Akihiko Takahashi
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最新提交年份：
2018
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英文摘要：
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 {\\sigma}-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.
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中文摘要：
本文提出了一种带跳跃的解耦正反向随机微分方程（FBSDE）的半解析近似方法。特别地，我们构造了一个由{sigma}有限补偿器的随机泊松测度驱动的FBSDE的渐近展开方法，以及围绕正向SDE的小方差极限的标准布朗运动。我们提供了一种半解析解技术及其误差估计，我们只需要求解一个线性常微分方程组。在强度有界的有限跳跃测度的情况下，该方法还可以处理与状态相关的非泊松跳跃，这与许多实际应用非常相关。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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