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Louisiana State University

1. Peng, Yun. Ito formula and Girsanov theorem on a new Ito integral.

Degree: PhD, Applied Mathematics, 2014, Louisiana State University

URL: etd-04082014-202541 ; https://digitalcommons.lsu.edu/gradschool_dissertations/4035

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 some results. In chapter 3, we prove the Ito formula for the Ayed-Kuo integral. In chapter 4, we prove the Girsanov theorem for this new stochastic integral. In chapter 5, we present an application of our results.

Subjects/Keywords: backward Brownian motion; Black Scholes formula; near martingale; adapted stochastic process; anticipating integral; Levy's characterization theorem; martingale; anticipating stochastic process; Brownian motion; Ito integral; instantly independent stochastic processes; backward adapted

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APA (6^{th} Edition):

Peng, Y. (2014). Ito formula and Girsanov theorem on a new Ito integral. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-04082014-202541 ; https://digitalcommons.lsu.edu/gradschool_dissertations/4035

Chicago Manual of Style (16^{th} Edition):

Peng, Yun. “Ito formula and Girsanov theorem on a new Ito integral.” 2014. Doctoral Dissertation, Louisiana State University. Accessed November 20, 2019. etd-04082014-202541 ; https://digitalcommons.lsu.edu/gradschool_dissertations/4035.

MLA Handbook (7^{th} Edition):

Peng, Yun. “Ito formula and Girsanov theorem on a new Ito integral.” 2014. Web. 20 Nov 2019.

Vancouver:

Peng Y. Ito formula and Girsanov theorem on a new Ito integral. [Internet] [Doctoral dissertation]. Louisiana State University; 2014. [cited 2019 Nov 20]. Available from: etd-04082014-202541 ; https://digitalcommons.lsu.edu/gradschool_dissertations/4035.

Council of Science Editors:

Peng Y. Ito formula and Girsanov theorem on a new Ito integral. [Doctoral Dissertation]. Louisiana State University; 2014. Available from: etd-04082014-202541 ; https://digitalcommons.lsu.edu/gradschool_dissertations/4035