Backward Stochastic Differential Equations (BSDEs) have been widely employed in various areas of social and natural sciences, such as the pricing and hedging of financial derivatives, stochastic optimal control problems, optimal stopping problems and gene expression. Most BSDEs cannot be solved analytically and thus numerical methods must be applied to approximate their solutions. There have been a variety of numerical methods proposed over the past few decades as well as many more currently being developed. For the most part, they exist in a complex and scattered manner with each requiring a variety of assumptions and conditions. The aim of the present work is thus to systematically survey various numerical methods for BSDEs, and in particular, compare and categorize them, for further developments and improvements. To achieve this goal, we focus primarily on the core features of each method based on an extensive collection of 333 references: the main assumptions, the numerical algorithm itself, key convergence properties and advantages and disadvantages, to provide an up-to-date coverage of numerical methods for BSDEs, with insightful summaries of each and a useful comparison and categorization.

翻译：向后随机微分方程（Backward Stochastic Differential Equations, BSDEs）已被广泛应用于社会与自然科学的多个领域，例如金融衍生品定价与对冲、随机最优控制问题、最优停止问题以及基因表达等。大多数BSDEs无法通过解析方法求解，因此必须借助数值方法来逼近其解。过去数十年间，研究者提出了多种数值方法，且当前仍有大量新方法正在开发之中。这些方法大多复杂且分散，各自依赖于不同的假设与条件。因此，本文旨在系统性地综述BSDEs的各种数值方法，并特别关注其比较与分类，以促进进一步的改进与发展。为实现这一目标，我们基于对333篇参考文献的广泛梳理，聚焦于每种方法的核心特征：主要假设、数值算法本身、关键收敛性质及优缺点，从而提供关于BSDEs数值方法的最新综述，并附有对每种方法的深刻总结以及实用的比较与分类。