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
Keywords	martingale exponential process local martingale Girsanov theorem Black-Scholes model ito integral
Date of Defense	2006-12-13
Availability	unrestricted
Abstract 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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