Qiu, JinniaoYao, Yao2021-03-192021-03-192021-03-14Yao, Y. (2021). Deep Learning-based Numerical Methods for Stochastic Partial Differential Equations and Applications (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.http://hdl.handle.net/1880/113159In 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.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.Education--FinanceEducation--MathematicsStatisticsmaster thesis10.11575/PRISM/38682