# On a Monotone Dynamic Approach to Optimal Stopping Problems for Continuous-Time Markov Chains

## TL;DR

This paper introduces a new monotone dynamic method for numerically solving optimal stopping problems related to perpetual American options driven by continuous-time Markov chains, ensuring convergence to the value function.

## Contribution

The paper presents a novel monotone sequence approach for pricing American options in Markov chain models, with minimal assumptions and proven convergence.

## Key findings

- The method effectively computes option values.
- Convergence of the sequence to the true value function is established.
- Applicable under minimal assumptions about payoffs and Markov chains.

## Abstract

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.