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：社会科学和自然科学的各个领域,例如金融衍生物的定价和套期保值、最佳最佳控制问题、最佳遏制问题和基因表达方式等,广泛采用后向异化方法(BSDEs),在社会科学和自然科学的各个领域,如金融衍生物的定价和套期保值、最佳控制问题、最佳遏制问题和基因表达方式等,大多数BSDEs无法以分析方式加以解决,因此,必须采用数字方法来估计解决办法的近似性。在过去几十年里,提出了各种数字方法,而且目前正在制订更多的数字方法。在大部分情况下,这些方法以复杂和分散的方式存在,每个方法都需要不同的假设和条件。因此,目前工作的目的是系统地调查BSDEs的各种数字方法,特别是对这些方法进行比较和分类,以便进一步发展和改进。为实现这一目标,我们主要侧重于基于广泛收集的333个参考文献的每一种方法的核心特征:主要假设、数字算法本身、关键趋同特性和利弊,以便为BSDEs提供最新的数字方法的覆盖面,并附有对每一种方法的深刻概述和有用的比较和分类。