Long Time Asymptotics For American Maximum Option With A Dividend-Paying Asset

Abstract

American maximum options provide minimum payo protections for the investors when the asset's price falls and bring more prots when the asset's price rises. It is interesting to explore the properties of them. In this paper, we pay attention to the long time behaviors of two optimal boundaries and the price function of American maximum option with a dividend-paying asset. We provide their long time behaviors by analyzing several integral equations related to the transformed optimal boundaries and the scaled price function and provide rigorous proofs for all results. Numerical examples are carried out to demonstrate the price and boundaries of American maximum option.