Structure of Optimal Stopping Strategies for American Type Options

Abstract

The paper presents results of theoretical studies of optimal stopping domains of American type options in discrete time. Sufficient conditions on the payoff functions and the price process for the optimal stopping domains to have one-threshold structure are given. We consider monotone, convex and inhomogeneous-in-time payoff functions. The underlying asset's price is modelled by an inhomogeneous discrete time Markov process.