This paper is concerned with the solution of the optimal stopping problem associated to the valuation of Perpetual American options driven by continuous time Markov chains. We introduce a new dynamic approach for the numerical pricing of this type of American options where the main idea is to build a monotone sequence of almost excessive functions that are associated to hitting times of explicit sets. Under minimal assumptions about the payoff and the Markov chain, we prove that the value function of an American option is characterized by the limit of this monotone sequence.
Markov chains; Optimal Stopping; American option pricing;
Laurent Miclo, and Stéphane Villeneuve, “On the forward algorithm for stopping problems on continuous-time Markov chains”, TSE Working Paper, n. 19-1009, April 2019.
TSE Working Paper, n. 19-1009, April 2019