An Investigation on the Existence and Uniqueness Analysis of the Optimal Exercise Boundary of American Put Option

Abstract

In this paper, we discuss the Hahn Banach fixed point theorem conditions on the optimal exercise boundary of American put option paying continuously dividend yield, to investigate whether its existence, uniqueness, and convergence are derived. In this respect, we consider the integral representation of the optimal exercise boundary which is extracted as a consequence of the Feynman-Kac formula. In order to prove the above features, we define a nonempty closed set in Banach space and prove that the proposed mapping in that space is contractive and onto mapping. At final, we demonstrate the ratio convergence of the mapping on the optimal exercise boundary.