Backward Stochastic Differential Equation

Backward Stochastic Differential Equations (BSDEs) are a powerful tool for solving various mathematical problems, particularly high-dimensional partial differential equations (PDEs), by reformulating them as stochastic control problems. Current research heavily focuses on developing efficient numerical methods for solving BSDEs, employing deep learning architectures like neural networks and tensor trains, often combined with genetic algorithms or other optimization techniques to improve convergence and accuracy. These advancements are significantly impacting fields like finance (e.g., option pricing), generative modeling (e.g., diffusion models), and control theory, enabling the solution of previously intractable high-dimensional problems.