英文标题：
《Anticipated Backward SDEs with Jumps and quadratic-exponential growth
drivers》
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作者：
Masaaki Fujii, Akihiko Takahashi
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最新提交年份：
2018
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英文摘要：
In this paper, we study a class of Anticipated Backward Stochastic Differential Equations (ABSDE) with jumps. The solution of the ABSDE is a triple $(Y,Z,\\psi)$ where $Y$ is a semimartingale, and $(Z,\\psi)$ are the diffusion and jump coefficients. We allow the driver of the ABSDE to have linear growth on the uniform norm of $Y$\'s future paths, as well as quadratic and exponential growth on the spot values of $(Z,\\psi)$, respectively. The existence of the unique solution is proved for Markovian and non-Markovian settings with different structural assumptions on the driver. In the former case, some regularities on $(Z,\\psi)$ with respect to the forward process are also obtained.
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中文摘要：
本文研究了一类带跳的预期倒向随机微分方程（ABSDE）。ABSDE的解是三元$（Y，Z，psi）$，其中$Y$是半鞅，$（Z，psi）$是扩散系数和跳跃系数。我们允许ABSDE的驱动因素在$Y$的未来路径的统一范数上具有线性增长，以及在$（Z，\\ psi）$的现货值上具有二次和指数增长。在不同的驱动结构假设下，证明了马尔可夫和非马尔可夫环境下唯一解的存在性。在前一种情况下，还得到了$（Z，，，psi）$上关于向前过程的一些正则性。
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分类信息：

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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