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Full-Text Articles in Physical Sciences and Mathematics
Ito Formula And Girsanov Theorem On A New Ito Integral, Yun Peng
Ito Formula And Girsanov Theorem On A New Ito Integral, Yun Peng
LSU Doctoral Dissertations
The celebrated Ito theory of stochastic integration deals with stochastic integrals of adapted stochastic processes. The Ito formula and Girsanov theorem in this theory are fundamental results which are used in many applied fields, in particular, the finance and the stock markets, e.g. the Black-Scholes model. In chapter 1 we will briefly review the Ito theory. In recent years, there have been several extension of the Ito integral to stochastic integrals of non-adapted stochastic processes. In this dissertation we will study an extension initiated by Ayed and Kuo in 2008. In Chapter 2 we review this new stochastic integral and …
The New Stochastic Integral And Anticipating Stochastic Differential Equations, Benedykt Szozda
The New Stochastic Integral And Anticipating Stochastic Differential Equations, Benedykt Szozda
LSU Doctoral Dissertations
In this work, we develop further the theory of stochastic integration of adapted and instantly independent stochastic processes started by Wided Ayed and Hui-Hsiung Kuo in [1,2]. We provide a first counterpart to the Itô isometry that accounts for both adapted and instantly independent processes. We also present several Itô formulas for the new stochastic integral. Finally, we apply the new Itô formula to solve a linear stochastic differential equations with anticipating initial conditions.
Stock Price Modeling And Insider Trading Theory, Jessica J. Guillory
Stock Price Modeling And Insider Trading Theory, Jessica J. Guillory
LSU Master's Theses
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 …