Abstract:
This article will approximate the solution of a class of high-dimensional reflection backward stochastic partial differential equations. The main difficulties are designing a backward discrete format and dealing with the singularity caused by the reflection term. Based on the deep separation method proposed by Christian Beck et al.1, we introduce and validate three algorithms that approximate the solutions of high-dimensional reflection backward stochastic partial differential equations, including one direct approximation and two penalty approximation methods. The numerical results indicate that within a relatively short operating time, the three approximation methods exhibit stable approximation results across 50 dimensions, with their relative error accuracy reaching a minimum of 10
−3.