论文标题
对角二次发电机的多维向后随机微分方程：一般结果
Multi-dimensional backward stochastic differential equations of diagonally quadratic generators: the general result
论文作者
论文摘要
本文致力于通过放松\ citet {Hutang2016Spa}的假设对生成器和末端值的假设，以对对角线二次发电机$ G（t，y，z）$的多维向后随机微分方程（BSDE）进行一般可溶性。更确切地说，发电机$ g（t，y，z）$可以在本地解决方案中具有更大的一般增长和连续性；在全球解决方案中，发电机$ g（t，y，z）$可能具有偏斜的次级偏差，但此外，第二个未知变量$ z $中的“严格和对角线上”二次增长，或者终端值可以取消结合，但生成器$ g（t，y，z）$在$上是$ $ z的$（$）$（$）$（生成器$ g $的$ g^i $仅取决于每个$ i = 1，\ cdots，n $的$ i $ -th $ z^i $。当终端值有限并且发电机$ G $受到某些一般假设的约束时，将在本地和全球解决方案上建立三个新结果。 When the terminal value is unbounded but is of exponential moments of arbitrary order, an existence and uniqueness result is given under the assumptions that the generator $g(t,y,z)$ is Lipschitz continuous in the first unknown variable $y$, and varies with the second unknown variable $z$ in a "diagonal" , "component-wisely convex or concave", and "quadratically growing" way, which seems成为具有无界终端值的二次BSDES系统的第一个一般溶解度。这通过一些新想法概括并增强了一些现有结果。
This paper is devoted to a general solvability of a multi-dimensional backward stochastic differential equation (BSDE) of a diagonally quadratic generator $g(t,y,z)$, by relaxing the assumptions of \citet{HuTang2016SPA} on the generator and terminal value. More precisely, the generator $g(t,y,z)$ can have more general growth and continuity in $y$ in the local solution; while in the global solution, the generator $g(t,y,z)$ can have a skew sub-quadratic but in addition "strictly and diagonally" quadratic growth in the second unknown variable $z$, or the terminal value can be unbounded but the generator $g(t,y,z)$ is "diagonally dependent" on the second unknown variable $z$ (i.e., the $i$-th component $g^i$ of the generator $g$ only depends on the $i$-th row $z^i$ of the variable $z$ for each $i=1,\cdots,n$ ). Three new results are established on the local and global solutions when the terminal value is bounded and the generator $g$ is subject to some general assumptions. When the terminal value is unbounded but is of exponential moments of arbitrary order, an existence and uniqueness result is given under the assumptions that the generator $g(t,y,z)$ is Lipschitz continuous in the first unknown variable $y$, and varies with the second unknown variable $z$ in a "diagonal" , "component-wisely convex or concave", and "quadratically growing" way, which seems to be the first general solvability of systems of quadratic BSDEs with unbounded terminal values. This generalizes and strengthens some existing results via some new ideas.
