论文标题
在路径依赖性的多维前向sdes上
On path-dependent multidimensional forward-backward SDEs
论文作者
论文摘要
本文将MA，Wu，Zhang，Zhang [11]的结果扩展到了依赖路径依赖性的多维前向随机微分方程（FBSDE）的背景。按照路径依赖性，我们的意思是，在时间t时向前sde的系数可以取决于向前过程的整个路径到时间t。当通过变分积分解决路径依赖性随机控制问题时，就会出现这种情况。我们分析的核心是在路径空间上构建一个脱钩的随机场。我们首先证明了在较小的时间间隔上的存在和脱钩场的独特性。然后，通过引入特征BSDE，我们表明，只要特征BSDE的解决方案保持界限，就可以通过将局部解决方案修补在一起来构建一个全局的去耦。最后，我们为路径依赖性前向下SDE提供了稳定性结果。
This paper extends the results of Ma, Wu, Zhang, Zhang [11] to the context of path-dependent multidimensional forward-backward stochastic differential equations (FBSDE). By path-dependent we mean that the coefficients of the forward-backward SDE at time t can depend on the whole path of the forward process up to time t. Such a situation appears when solving path-dependent stochastic control problems by means of variational calculus. At the heart of our analysis is the construction of a decoupling random field on the path space. We first prove the existence and the uniqueness of decoupling field on small time interval. Then by introducing the characteristic BSDE, we show that a global decoupling field can be constructed by patching local solutions together as long as the solution of the characteristic BSDE remains bounded. Finally, we provide a stability result for path-dependent forward-backward SDEs.
