Deep branching solution of financial partial differential equations

• Main Author: Wang, Yiran
• Other Authors: Nicolas Privault
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2023
• Subjects: Engineering::Mathematics and analysis
• Online Access: https://hdl.handle.net/10356/166540
• Institution: Nanyang Technological University

This paper compares the performance of the deep branching method against two other popular deep learning methods, deep BSDE and deep Galerkin, for solving partial differential equations (PDEs) in finance. The methods were tested on different financial models including Bachelier, Black-Scholes on European options, power options, and forward contracts. Results showed that the deep branching method outperformed both deep BSDE and deep Galerkin in terms of accuracy and stability, but further testing is needed to compare the runtime in dealing with forward contract and power options. Overall, this study highlights the efficiency of the deep branching method as a general-purpose numerical method for solving PDEs, and its potential for broader applications in finance and beyond.