Master of Science (MS)
The mathematical study of stock price modeling using Brownian motion and stochastic calculus is a relatively new field. The randomness of financial markets, geometric brownian motions, martingale theory, Ito's lemma, enlarged filtrations, and Girsanov's theorem provided the motivation for a simple characterization of the concepts of stock price modeling. This work presents the theory of stochastic calculus and its use in the financial market. The problems on which we focus are the models of an investor's portfolio of stocks with and without the possibility of insider trading, opportunities for fair pricing of an option, enlarged filtrations, consumptions, and admissibility. This survey has two parts. The first part explores the theoretical aspects of stochastic calculus, and the second part shows its application in predicting stock prices and the wealth of an investor's portfolio.
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Release the entire work immediately for access worldwide.
Guillory, Jessica J., "Stock price modeling and insider trading theory" (2003). LSU Master's Theses. 927.