Numerical methods for model-free pricing in finance, optimal transport, and cyber risk management

• Main Author: Xiang, Qikun
• Other Authors: Ariel Neufeld
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2023
• Subjects: Science::Mathematics::Applied mathematics::Optimization; Science::Mathematics::Probability theory
• Online Access: https://hdl.handle.net/10356/172791
• Institution: Nanyang Technological University

This thesis presents results from five projects that I have worked on with my collaborators throughout my PhD. The thesis is divided into three parts. Part 1 of the thesis deals with the computation of model-free price bounds of financial derivatives and presents the numerical methods we have developed for this problem. The theme of Part 2 of the thesis is about the numerical methods that we have developed for problems related to optimal transport. Specifically, Part 2 deals with the multi-marginal optimal transport problem, the two-stage distributionally robust optimization problem with marginal constraints, and the matching for teams problem which comes from theoretical economics. Finally, Part 3 of the thesis focuses on the cyber risk insurance market and presents our Bonus-Malus based cyber risk insurance model as well as the numerical method that we have developed for analyzing it.