A convolution method for numerical solution of backward stochastic differential equations
Abstract
We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and computed using the fast Fourier transform (FFT). The problem of error control is addressed and a local error analysis is provided. We consider the extension of the method to forward-backward stochastic differential equations (FBSDEs) and reflected FBSDEs. Numerical examples are considered from finance demonstrating the performance of the method.
Keywords
Cite
@article{arxiv.1304.1783,
title = {A convolution method for numerical solution of backward stochastic differential equations},
author = {Cody Blaine Hyndman and Polynice Oyono Ngou},
journal= {arXiv preprint arXiv:1304.1783},
year = {2015}
}
Comments
29 pages, 4 figures; Revised (Version 3): Editorial changes; Additional references; Section 2: Removed derivation of implicit Euler scheme; Section 3: Further details on numerical implementation and algorithm; Section 4: Improved Error Analysis by adding new Theorem 4.2 on stability and convergence; Section 6: improved discussion of examples and numerical results