A Fourier interpolation method for numerical solution of FBSDEs: Global convergence, stability, and higher order discretizations
Abstract
The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs), introduced in [21], uses a uniform space grid. In this paper we utilize a tree-like spatial discretization that approximates the BSDE on the tree, so that no spatial interpolation procedure is necessary. In addition to suppressing extrapolation error, leading to a globally convergent numerical solution for the FBSDE, we provide explicit convergence rates. On this alternative grid the conditional expectations involved in the time discretization of the BSDE are computed using Fourier analysis and the fast Fourier transform (FFT) algorithm. The method is then extended to higher-order time discretizations of FBSDEs. Numerical results demonstrating convergence are presented using a commodity price model, incorporating seasonality, and forward prices.
Keywords
Cite
@article{arxiv.1410.8595,
title = {A Fourier interpolation method for numerical solution of FBSDEs: Global convergence, stability, and higher order discretizations},
author = {Polynice Oyono Ngou and Cody Hyndman},
journal= {arXiv preprint arXiv:1410.8595},
year = {2022}
}
Comments
28 pages, 8 figures; Previously titled 'Global convergence and stability of a convolution method for numerical solution of BSDEs' (1410.8595v1)