Deep Learning-based Numerical Methods for Stochastic Partial Differential Equations and Applications
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2021-03-14
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Abstract
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.
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Yao, 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.