Open AccessAn investigation on the existence and uniqueness analysis of the optimal exercise boundary of American put option
Author(s) -
Davood Ahmadian,
Akbar Ebrahimi,
Karim Ivaz,
Mariyan Milev
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2104095a
Subject(s) - mathematics , uniqueness , banach space , boundary (topology) , convergence (economics) , representation (politics) , pure mathematics , fixed point , mathematical analysis , fixed point theorem , put option , finance , politics , political science , law , economics , economic growth
In this paper, we discuss the 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 is contractive and onto. At final, we illustrate the ratio convergence of the mapping on the optimal exercise boundary.