Conic optimization with applications in finance and approximation theory

This dissertation explores conic optimization techniques with applications in the fields of finance and approximation theory. One of the most general types of conic optimization problems is the so-called generalized moment problem (GMP), which plays a fundamental part in this work. While being a powerful modeling framework, the GMP is notoriously difficult to solve. Semidefinite programming problems (SDPs) can be used to define approximation hierarchies for the GMP. The thesis includes an analysis of an interior point algorithm for SDPs, as well as a convergence analysis of an approximation hierarchy for the GMP defined over special sets. Additionally, the dissertation investigates the problem of pricing options that depend on multiple underlyings, which can be modeled as a GMP. Finally, the dissertation applies tools from conic optimization to address a classical question in approximation theory.