| Summary: | 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.
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