Finite dimensional realizations for term structure models driven by semimartingales [Elektronische Ressource] / von Stefan Tappe

Finite Dimensional Realizations for Term StructureModels driven by SemimartingalesDISSERTATIONzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat.)im Fach Mathematikeingereicht an derMathematisch-Naturwissenschaftlichen Fakultat IIder Humboldt-Universitat zu BerlinvonHerrn Dipl.-Math. Stefan Tappegeboren am 7. Februar 1977 in DetmoldPrasident der Humboldt-Universitat zu Berlin: Prof. Dr. Hans Jurgen Promel Dekan der Mathematisch-Naturwissenschaftlichen Fakultat II:Prof. Dr. Uwe KuchlerGutachter:1. Prof. Dr. Uwe Kuchler2. Prof. Tomas Bjork, Ph.D.3. Prof. Dr. Jan Kallseneingereicht am: 5. Juli 2005Tag der mundlichen Prufung: 7. November 2005 AbstractLet f(t,T) be a term structure model of Heath-Jarrow-Morton typedf(t,T) =(t,T)dt+(t,T)dX ,tdrivenbyamultidimensionalsemimartingaleX.Ourobjectiveistostudytheexistenceof nite dimensional realizations for equations of this kind. Choosing the class ofGrigelionis processes (including in particular Levy processes) as driving processes, weapproach this problem from two di erent directions.Extending the ideas from di erential geometry in Bj ork and Svensson (2001), weshow that the criterion for the existence of nite dimensional realizations, proven intheaforementionedpaper,stillservesasanecessaryconditioninoursetup.Thisresultis applied to concrete volatility structures.