AI and the World's Hard Problems · Mathematics · arXiv · 2026-10-20
A Deep Backward Scheme for Reflected BSDEs via Penalization : Approximation and Convergence Analysis
This work tackles the numerical solution of Markovian reflected backward stochastic differential equations. The reflection constraint is replaced by penalized BSDEs, which neural networks approximate backward in time, with error estimates for both the value and control processes. The value component has a mean-square error of order O(|π|^{1/3}), and numerical experiments on a reflected BSDE and American option problems illustrate the scheme.