标题： 路径依赖的FBSDEs的离散化方案 显示英文标题

标题： A discretization scheme for path-dependent FBSDEs

摘要： 本文研究了具有路径依赖系数的前向-后向随机微分方程（FBSDEs）的离散化方案。 我们展示了Picard型迭代收敛到FBDSE解，并提供了其收敛速率。 据我们所知，这是关于路径依赖FBSDEs离散化方案的第一个结果。 利用这一结果，我们建立了求解二阶抛物型路径依赖偏微分方程的数值方法。 为此，采用了鞅表示定理的弱逼近（Cont, Rama, and Yi Lu. "Weak approximation of martingale representations." Stochastic Processes and their Applications 2016）。 我们的结果推广了（Bender, Christian, and Robert Denk. "A forward scheme for backward SDEs." Stochastic processes and their applications, 2007）中对于马尔可夫情形的方案。 显示英文摘要

摘要： This paper studies a discretization scheme for solutions to forward-backward stochastic differential equations (FBSDEs) with path-dependent coefficients. We show the convergence of the Picard-type iteration to the FBDSE solution and provide its convergence rate. To the best of our knowledge, this is the first result of discretization scheme for path-dependent FBSDEs. Using this result, we establish a numerical method for solutions to second-order parabolic path-dependent partial differential equations. To achieve this, weak approximation of martingale representation theorem (Cont, Rama, and Yi Lu. ``Weak approximation of martingale representations." Stochastic Processes and their Applications 2016) is employed. Our results generalize the scheme for Markovian cases in (Bender, Christian, and Robert Denk. ``A forward scheme for backward SDEs." Stochastic processes and their applications, 2007)