On moment conditions for the Girsanov Theorem

In this dissertation, the well-known Girsanov Theorem will be proved under a set of moment conditions on exponential processes. Our conditions are motivated by the desire to avoid using the local martingale theory in the proof of the Girsanov Theorem. Namely, we will only use the martingale theory to prove the Girsanov Theorem. Many sufficient conditions for the validity of the Girsanov Theorem have been found since the publication of the result by Girsanov in 1960. We will compare our conditions with some of these conditions. As an application of the Girsanov Theorem, we will show the nonexistence of an arbitrage in a market and will also explain a simplified version of Black-Scholes model.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2006

Author dc:creator

• Lee, See Keong

• martingale
• exponential process
• local martingale
• Girsanov theorem
• Black-Scholes model
• ito integral

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-11162006-111635
https://repository.lsu.edu/gradschool_dissertations/998

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-1997