Optimal control problem for American put option
by Sun, Junjian, Ph.D., WASHINGTON STATE UNIVERSITY, 2011, 80 pages; 3460439

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.
 
AdviserHongming Yin
SchoolWASHINGTON STATE UNIVERSITY
SourceDAI/B 72-09, p. , Jul 2011
Source TypeDissertation
SubjectsApplied mathematics; Mathematics
Publication Number3460439
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