On Tuesday, 4 July 2023 at 13:30pm, Felix Kirschner will defend his PhD thesis entitled “Conic Optimization with Applications in Finance and Approximation Theory” in the Auditorium in the Cobbenhagen building of Tilburg University.
His supervisors are Prof. Dr. Etienne de Klerk and dr. Juan Vera Lizcano. A livestream of this PhD defense can be followed via https://www.tilburguniversity.edu/current/events/phd-defense-fc-kirschner.
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.
Felix Constantin Kirschner (Hof, Germany, 1993) received his bachelor’s and master’s degrees in “Wirtschaftsmathematik” (hybrid program in applied mathematics, computer science and economics) from the University of Cologne (2016 & 2019). In 2019 he joined the Department of Econometrics and Operations Research at Tilburg University as a PhD candidate as part of the Marie Skłodowska-Curie Innovative Training Network POEMA.
