Optimal stopping of strong Markov processes

Sören Christensen, Paavo Salminen, Bao Quoc Ta

Published 2012-03-21, updated 2012-04-02Version 2

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.