发表机构
Department of Mathematics, Saarland University（萨尔兰大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种深度BSDE方法的变体，在无需小时间区间、单调性或弱耦合假设下，为强耦合FBSDEs建立后验收敛结果，并通过数值实验验证了方法的有效性。
AI 中文摘要
我们研究了E等人（2017，2018）提出的深度BSDE方法的一种变体。关键创新在于，我们为强耦合正倒向随机微分方程（FBSDEs）的近似建立了一个后验收敛结果，即我们的结果在不需要文献中深度BSDE方法通常施加的小时间区间、单调性或弱耦合假设的情况下成立。相反，我们依赖于系数的光滑性假设，并覆盖了BSDE向SDE的耦合依赖于后向分量$Y$和控制分量$Z$的FBSDEs。数值实验验证了理论结果，并展示了所提出方法的适用性。
英文摘要
We investigate a variant of the deep BSDE method introduced by E et al. (2017, 2018). The key novelty is that we establish an a-posteriori convergence result for the approximation of strongly coupled forward-backward stochastic differential equations (FBSDEs), i.e., our result holds without any assumptions on small time horizons, monotonicity or weak coupling that are typically imposed in the literature on the deep BSDE method. Instead, we rely on smoothness assumptions on the coefficients and cover FBSDEs in which the coupling of the BSDE into the SDE depends on both the backward component $Y$ and the control component $Z$. Numerical experiments illustrate the theoretical results and demonstrate the applicability of the proposed approach.
Comments38 pages, 4 figures
