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：倒向随机微分方程（BSDEs）已广泛应用于自然与社会科学多个领域，例如金融衍生品定价与对冲、随机最优控制问题、最优停时问题以及基因表达。由于大多数BSDEs无法解析求解，必须采用数值方法对其解进行逼近。过去数十年间涌现出多种数值方法，且当前仍有大量新方法正处于研发阶段。这些方法大多复杂且离散，各自需要不同的假设条件。因此，本文旨在系统综述BSDEs的各类数值方法，特别注重对其进行分类与比较，以促进后续改进与发展。为实现这一目标，我们基于对333篇参考文献的广泛梳理，重点关注各方法的核心特征：主要假设、数值算法本身、关键收敛性质以及优缺点，从而提供关于BSDEs数值方法的最新综述，附有对每种方法的深入总结，并给出有效的比较与分类。