Resolvent-techniques for multiple exercise problems

Abstract

Abstract. We study optimal multiple stopping of strong Markov processes with random refraction periods. The refraction periods are assumed to be exponentially distributed with a common rate and independent of the underlying dynamics. Our main tool is using the resolvent operator. In the rst part, we reduce in nite stopping problems to ordinary ones in a general strong Markov setting. This leads to explicit solutions for wide classes of such problems. Starting from this result, we analyze problems with nitely many exercise rights and explain solution methods for some classes of problems with underlying L evy and di usion processes, where the optimal characteristics of the problems can be identified more explicitly. We illustrate the main results with explicit examples.