Title page for ETD etd-11162006-111635

Type of Document Dissertation
Author Lee, See Keong
Author's Email Address sklin_04@hotmail.com
URN etd-11162006-111635
Title On Moment Conditions for the Girsanov Theorem
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Hui-Hsiung Kuo Committee Chair
Ambar Sengupta Committee Member
Augusto Nobile Committee Member
Jorge Morales Committee Member
Robert Perlis Committee Member
Seung-Jong Park Dean's Representative
  • martingale
  • exponential process
  • local martingale
  • Girsanov theorem
  • Black-Scholes model
  • ito integral
Date of Defense 2006-12-13
Availability unrestricted
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.
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