Optimal stopping of strong Markov processes

TL;DR

This paper characterizes the value function and optimal stopping times for a broad class of Markov processes, extending recent Lévy process results using $eta$-excessive functions and providing various examples.

Contribution

It introduces a new approach to optimal stopping problems for general Markov processes using $eta$-excessive functions, inspired by Wiener-Hopf factorization techniques.

Findings

Characterization of the value function for general Markov processes.

Representation of $eta$-excessive functions as expected suprema.

Application to various examples of Markov processes.

Abstract

We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings for L\'evy processes obtained essentially via the Wiener-Hopf factorization. The main ingredient in our approach is the representation of the $\beta$-excessive functions as expected suprema. A variety of examples is given.