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：倒向随机微分方程已在社会和自然科学的多个领域得到广泛应用，例如金融衍生品定价与对冲、随机最优控制问题、最优停时问题及基因表达。大多数BSDE无法解析求解，因此必须采用数值方法逼近其解。过去数十年间，已有多种数值方法被提出，且当前仍有大量方法正在开发中。这些方法大多复杂且分散，各自需要不同的假设与条件。因此，本工作旨在系统性地综述BSDE的各类数值方法，特别是对它们进行比较与分类，以促进进一步的发展与改进。为实现此目标，我们基于333篇参考文献，着重关注每种方法的核心特征：主要假设、数值算法本身、关键收敛性质及其优缺点，从而提供对BSDE数值方法的最新覆盖，并给出每类方法的深刻总结以及有用的比较与分类。