386
Views
35
CrossRef citations to date
0
Altmetric
Section B

Multilevel Monte Carlo method with applications to stochastic partial differential equations

&
Pages 2479-2498 | Received 31 Oct 2011, Accepted 07 Jun 2012, Published online: 03 Jul 2012
 

Abstract

In this work, the approximation of Hilbert-space-valued random variables is combined with the approximation of the expectation by a multilevel Monte Carlo (MLMC) method. The number of samples on the different levels of the multilevel approximation are chosen such that the errors are balanced. The overall work then decreases in the optimal case to O(h −2) if h is the error of the approximation. The MLMC method is applied to functions of solutions of parabolic and hyperbolic stochastic partial differential equations as needed, for example, for option pricing. Simulations complete the paper.

2010 AMS Subject Classifications:

Acknowledgements

This research was supported in part by the European Research Council under grant ERC AdG 247277. The authors thank the anonymous referee for very helpful comments.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.