A Review of Tree-based Approaches to solve Forward-Backward Stochastic Differential Equations

Abstract

In this work, we study solving (decoupled) forward-backward stochastic differential equations (FBSDEs) numerically using the regression trees. Based on the general theta-discretization for the time-integrands, we show how to efficiently use regression tree-based methods to solve the resulting conditional expectations. Several numerical experiments including high-dimensional problems are provided to demonstrate the accuracy and performance of the tree-based approach. For the applicability of FBSDEs in financial problems, we apply our tree-based approach to the Heston stochastic volatility model, the high-dimensional pricing problems of a Rainbow option and an European financial derivative with different interest rates for borrowing and lending.

References in corpus (3)

• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
• A regression-based Monte Carlo method to solve backward stochastic differential equations
• On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations

Cited by in corpus (1)

• Deep learning algorithms for solving high dimensional nonlinear backward stochastic differential equations