A class of optimal stopping problems for Markov processes

TL;DR

This paper investigates a specific class of optimal stopping problems for Markov processes, establishing the convexity of the value function and characterizing the optimal stopping boundary, along with a method to compute it.

Contribution

It introduces a new approach to determine the optimal boundary function for a class of Markov process stopping problems, emphasizing convexity properties.

Findings

Value function is convex.

Existence of a boundary function for optimal stopping.

A method to compute the boundary function.

Abstract

Our purpose is to study a particular class of optimal stopping problems for Markov processes. We justify the value function convexity and we deduce that there exists a boundary function such that the smallest optimal stopping time is the first time when the Markov process passes over the boundary depending on time. Moreover, we propose a method to find the optimal boundary function.