Numerical Methods for Backward Stochastic Differential Equations: A Survey

Backwards Stochastic Differential Equations (BSDEs) have been widely employed in various areas of applied and financial mathematics. In particular, BSDEs appear extensively in the pricing and hedging of financial derivatives, stochastic optimal control problems and optimal stopping problems. Most BSDEs cannot be solved analytically and thus numerical methods must be applied in order to approximate their solutions. There have been many numerical methods proposed over the past few decades, for the most part, in a complex and scattered manner, with each requiring a variety of different and similar assumptions and conditions. The aim of the present paper is thus to systematically survey various numerical methods for BSDEs, and in particular, compare and categorise them. To this end, we focus on the core features of each method: the main assumptions, the numerical algorithm itself, key convergence properties and advantages and disadvantages, in order to provide an exhaustive up-to-date coverage of numerical methods for BSDEs, with insightful summaries of each and useful comparison and categorization.