Forward Backward Stochastic Differential Equation

Forward-backward stochastic differential equations (FBSDEs) are a powerful mathematical framework for solving stochastic control problems and related challenges, primarily aiming to find solutions to coupled systems of stochastic differential equations evolving both forward and backward in time. Current research heavily utilizes deep learning methods, particularly neural networks, to approximate solutions, especially in high-dimensional settings, with a focus on efficient algorithms for McKean-Vlasov FBSDEs and applications in areas like optimal investment and opinion dynamics. This approach offers significant advancements in tackling complex problems previously intractable due to the "curse of dimensionality," impacting fields such as finance, control theory, and machine learning.