Deep Learning-based Numerical Methods for Stochastic Partial Differential Equations and Applications

In this thesis, we are concerned with approximating solutions of stochastic partial differential equations (SPDEs) and their applications. Inspired by Huré, Pham, and Warin [15], we propose and study the deep learning-based methods for both the forward and backward SPDEs. In particular, the forward SPDEs may allow for Neumann boundary conditions. We also prove the convergence analysis of the proposed algorithms. The numerical results indicate that the performance of the algorithm is quite effective for solving the SPDEs, even in high-dimensional cases. The applications include various pricing problems under exchange rate target zone models as well as under rough volatility models.

Name thesis:degree_name

Master of Science (MSc)

Discipline thesis:degree_discipline

Mathematics & Statistics

Grantor dc:publisher.institution

Science

Year dc:date.issued

2021

Author dc:creator

• Yao, Yao

Advisor dc:contributor.advisor

• Qiu, Jinniao

Committee members dc:contributor.committeemember

• Ware, Antony
• Badescu, Alexandru

Statement dc:rights

• University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.

DOI

http://dx.doi.org/10.11575/PRISM/38682

OAI identifier oai:identifier

oai:ucalgary.scholaris.ca:1880/113159