A generalized scheme for BSDEs based on derivative approximation and its error estimates
For researchers in numerical analysis and stochastic processes, this work offers a flexible framework for solving BSDEs, though it is incremental as it extends existing interpolation techniques.
This paper proposes a generalized numerical scheme for BSDEs using Lagrange interpolation for derivative approximation, achieving various stability and convergence orders by adjusting sample point distribution. A condition for convergence is provided.
In this paper we propose a generalized numerical scheme for backward stochastic differential equations(BSDEs). The scheme is based on approximation of derivatives via Lagrange interpolation. By changing the distribution of sample points used for interpolation, one can get various numerical schemes with different stability and convergence order. We present a condition for the distribution of sample points to guarantee the convergence of the scheme.