{"id":{"repo_id":"freiburg-diss","oai_identifier":"oai:freidok.uni-freiburg.de:2067"},"canonical_url":"https://search.dev.ndltd.org/etd/freiburg-diss/oai:freidok.uni-freiburg.de:2067","repository":{"repo_id":"freiburg-diss","name":"University of Freiburg","base_url":"https://freidok.uni-freiburg.de/oai/oai2.php"},"display":{"title":"Comparison of semimartingales and Lévy processes with applications to financial mathematics","abstract":"In this thesis we derive convex and increasing convex type orderings for multivariate semimartingales and the finite-dimensional distributions of Lévy processes. Appropriate ordering of the semimartingale characteristics implies ordering of the processes. We derive the propagation of order property for some classes of multivariate diffusions and mulitvariate diffusions with jumps. Furthermore, we obtain cut and domination criteria for Lévy measures and orderings for mixing type distributions. We apply the ordering results to obtain non-trivial bounds for European option prices in incomplete market models, to compare martingale measures and to compare path-dependent options.","abstract_html":"In this thesis we derive convex and increasing convex type orderings for multivariate semimartingales and the finite-dimensional distributions of Lévy processes. Appropriate ordering of the semimartingale characteristics implies ordering of the processes. We derive the propagation of order property for some classes of multivariate diffusions and mulitvariate diffusions with jumps. Furthermore, we obtain cut and domination criteria for Lévy measures and orderings for mixing type distributions. We apply the ordering results to obtain non-trivial bounds for European option prices in incomplete market models, to compare martingale measures and to compare path-dependent options.","abstract_has_math":false,"creators":["Bergenthum, Jan"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Rüschendorf, Ludger"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T02:22:33Z","subjects":["Ordnungsfortsetzungseigenschaft","konvexe Ordnung","richtungskonvexe Ordnung","supermodulare Ordnung","propagation of order property","convex order","directionally convex order","supermodular order"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://freidok.uni-freiburg.de/data/2067","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rüschendorf, Ludger"]},{"key":"dc:creator","label":"Author","values":["Bergenthum, Jan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["DoctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Ordnungsfortsetzungseigenschaft","konvexe Ordnung","richtungskonvexe Ordnung","supermodulare Ordnung","propagation of order property","convex order","directionally convex order","supermodular order"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we derive convex and increasing convex type orderings for multivariate semimartingales and the finite-dimensional distributions of Lévy processes. Appropriate ordering of the semimartingale characteristics implies ordering of the processes. We derive the propagation of order property for some classes of multivariate diffusions and mulitvariate diffusions with jumps. Furthermore, we obtain cut and domination criteria for Lévy measures and orderings for mixing type distributions. We apply the ordering results to obtain non-trivial bounds for European option prices in incomplete market models, to compare martingale measures and to compare path-dependent options.","In der Arbeit werden Ordnungen konvexen und wachsend konvexen Typs für multivariate Semimartingale und die endlich-dimensionalen Verteilungen von multivariaten Lévy Prozessen hergeleitet. Geeignete Ordnung der Semimartingalcharakteristiken impliziert Ordnung der Prozesse. Für einige Klassen von multivariaten Diffusionen und multivariaten Diffusionen mit Sprüngen wird die Ordnungsfortsetzungseigenschaft nachgewiesen. Des Weiteren werden Schnitt- und Dominiertheitskriterien für Lévy Maße und Ordnungsresultate für Mischungsdarstellungen hergeleitet. Mit Hilfe der Ordnungsresultate werden nicht-triviale Schranken für Europäische Optionspreise in unvollständigen Marktmodellen hergeleitet, Ordnungen von Martingalmaßen nachgewiesen und pfadabhängigen Optionen verglichen."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Comparison of semimartingales and Lévy processes with applications to financial mathematics","Vergleich von Semimartingalen und Lévy Prozessen mit Anwendungen in der Finanzmathematik"]}]}],"canonical_facts":{"dc:contributor":["Rüschendorf, Ludger"],"dc:creator":["Bergenthum, Jan"],"dc:description.abstract":["In this thesis we derive convex and increasing convex type orderings for multivariate semimartingales and the finite-dimensional distributions of Lévy processes. Appropriate ordering of the semimartingale characteristics implies ordering of the processes. We derive the propagation of order property for some classes of multivariate diffusions and mulitvariate diffusions with jumps. Furthermore, we obtain cut and domination criteria for Lévy measures and orderings for mixing type distributions. We apply the ordering results to obtain non-trivial bounds for European option prices in incomplete market models, to compare martingale measures and to compare path-dependent options.","In der Arbeit werden Ordnungen konvexen und wachsend konvexen Typs für multivariate Semimartingale und die endlich-dimensionalen Verteilungen von multivariaten Lévy Prozessen hergeleitet. Geeignete Ordnung der Semimartingalcharakteristiken impliziert Ordnung der Prozesse. Für einige Klassen von multivariaten Diffusionen und multivariaten Diffusionen mit Sprüngen wird die Ordnungsfortsetzungseigenschaft nachgewiesen. Des Weiteren werden Schnitt- und Dominiertheitskriterien für Lévy Maße und Ordnungsresultate für Mischungsdarstellungen hergeleitet. Mit Hilfe der Ordnungsresultate werden nicht-triviale Schranken für Europäische Optionspreise in unvollständigen Marktmodellen hergeleitet, Ordnungen von Martingalmaßen nachgewiesen und pfadabhängigen Optionen verglichen."],"dc:format.medium":["application/pdf"],"dc:subject":["Ordnungsfortsetzungseigenschaft","konvexe Ordnung","richtungskonvexe Ordnung","supermodulare Ordnung","propagation of order property","convex order","directionally convex order","supermodular order"],"dc:title":["Comparison of semimartingales and Lévy processes with applications to financial mathematics","Vergleich von Semimartingalen und Lévy Prozessen mit Anwendungen in der Finanzmathematik"],"dc:type":["DoctoralThesis"]},"updated_at":"2026-07-24T02:22:33Z"}