Dissertation
Optimal Control Problem for American Put Option
Doctor of Philosophy (PhD), Washington State University
01/2011
Handle:
https://hdl.handle.net/2376/2924
Abstract
In the dissertation, we study an inverse free boundary problem associated with the American put option, where the free boundary is called the early exercise boundary and separates the option holding region from the stopping region. The reverse problem is derived from the Black-Scholes equation to recover the implied volatility from the current market option price. Our goal is to identify the coefficient of the second-order partial derivative of the Black-Scholes equation. Indeed, the reverse problem is ill-posed. Optimal control method of PDEs is often used to regulate this type of problems. We use the implied volatility function as the control parameter and prove the existence and convergence of the minimizer. We also discuss the necessary optimality condition for the optimal control. At the end, a numerical method is presented and rigorous mathematical analysis of the corresponding discrete problem is carried out.
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Details
- Title
- Optimal Control Problem for American Put Option
- Creators
- Junjian Sun
- Contributors
- Hongming Yin (Advisor)Haijun Li (Committee Member)Alex Khapalov (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 80
- Identifiers
- 99900581458201842
- Language
- English
- Resource Type
- Dissertation