Dependent FBSDEs

Dependent forward-backward stochastic differential equations (FBSDEs) provide a powerful framework for solving complex stochastic control problems and high-dimensional partial differential equations (PDEs). Current research focuses on developing efficient numerical methods, particularly leveraging deep learning architectures like deep neural networks and genetic algorithms, to overcome the computational challenges associated with high dimensionality and nonlinearity. These advancements are significantly improving the ability to solve problems in diverse fields, including finance (option pricing), robotics (multi-agent control), and opinion dynamics, where traditional methods often fall short. The resulting algorithms demonstrate improved accuracy and efficiency compared to existing techniques.