Optimal stopping via measure transformation: the Beibel–Lerche approach

Abstract

Optimal stopping of diffusions and related processes is usually done by solving a free boundary problem. In this paper, we propagate an alternative way, which has already been described in two earlier papers of Beibel and Lerche; we call it the B–L approach. It can be viewed as optimal stopping via measure transformation. While we emphasized in Beibel and Lerche a rather algebraic view, we describe here more the analytic side of the approach. Finally, it is related to some recent Jamshidian's results on a duality in optimal stopping.