Stochastic grid bundling method for backward stochastic differential equations

ABSTRACT

In this work, we apply the Stochastic Grid Bundling Method (SGBM) to numerically solve backward stochastic differential equations (BSDEs). The SGBM algorithm is based on conditional expectations approximation by means of bundling of Monte Carlo sample paths and a local regress-later regression within each bundle. The basic algorithm for solving the backward stochastic differential equations will be introduced and an upper error bound is established for the local regression. A full error analysis is also conducted for the explicit version of our algorithm and numerical experiments are performed to demonstrate various properties of our algorithm.

KEYWORDS:

• SGBM
• BSDE
• Monte-Carlo
• regress-later
• bundling

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 91G60

Acknowledgments

The authors would like to thank VORtech, BV, for their help and advice for this work and the anonymous reviewers for their valuable advice for improving this work.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ki Wai Chau  http://orcid.org/0000-0002-6198-1178

Notes

1. The situation of $\frac{0}{0}$ should be understood as 0 and $\frac{K}{0}$ as ∞ in the rest of this article.

Additional information

Funding

This work is supported by EU Framework Programme for Research and Innovation Horizon 2020 (H2020-MSCA-ITN-2014, Project 643045, ‘EID WAKEUPCALL’).