具有跳跃和二次指数增长驱动因素的预期后向随机微分方程
Anticipated Backward SDEs with Jumps and quadratic-exponential growth drivers
摘要：
本文研究了一类带跳的期望倒向随机微分方程（ABCD）. AB矩阵的解是一个三元组$(Y,Z,ψ)$，其中$Y$是一个半鞅，$(Z,ψ)$是扩散系数和跳跃系数。我们允许ABBYY的驱动程序在$Y$未来路径的一致范数上具有线性增长，以及分别在$(Z,ψ)$的现货值上具有二次和指数增长。证明了在不同的驱动器结构假设条件下，马尔可夫和非马尔可夫情形下唯一解的存在性。在前一种情况下，还得到了关于前向过程的一些非线性$(Z,ψ)$。
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 $(Y,Z,ψ)$ where $Y$ is a semimartingale, and $(Z,ψ)$ 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 $(Z,ψ)$, 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 $(Z,ψ)$ with respect to the forward process are also obtained.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
