Comparison of semimartingales and Lévy processes with applications to financial mathematics

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.

Author dc:creator

• Bergenthum, Jan

Contributors dc:contributor

• Rüschendorf, Ludger

• Ordnungsfortsetzungseigenschaft
• konvexe Ordnung
• richtungskonvexe Ordnung
• supermodulare Ordnung
• propagation of order property
• convex order
• directionally convex order
• supermodular order

Repository record source_url

https://freidok.uni-freiburg.de/data/2067

OAI identifier oai:identifier

oai:freidok.uni-freiburg.de:2067