An efficient third-order scheme for BSDEs based on nonequidistant difference scheme
It provides a more efficient high-order method for solving BSDEs, which are important in finance and stochastic control, but the improvement is incremental over existing schemes.
This paper proposes a third-order numerical scheme for backward stochastic differential equations (BSDEs) using a 3-point Gauss-Hermite quadrature and fully nested spatial grids, achieving reduced computational complexity and demonstrated third-order accuracy on several examples.
In this paper we propose an efficient third-order numerical scheme for backward stochastic differential equations(BSDEs). We use 3-point Gauss-Hermite quadrature rule for approximation of the conditional expectation and avoid spatial interpolation by setting up a fully nested spatial grid and using the approximation of derivatives based on non-equidistant sample points. As a result, the overall computational complexity is reduced significantly. Several examples show that the proposed scheme is of third-order and very efficient.