On the Riesz Representation for Optimal Stopping Problems

Abstract

In this thesis we summarize results about optimal stopping problems analyzed with the Riesz representation theorem. Furthermore we consider two examples: Firstly the optimal investment problem with an underlying d-dimensional geometric Brow- nian motion. We derive formulas for the optimal stopping boundaries for the one- and two-dimensional cases and we find a numerical approximation for the boundary in the two-dimensional problem. After this we change the focus to a space-time one-dimensional geometric Brownian motion with finite time horizon. We use the Riesz representation theorem to approximate the optimal stopping boundaries for three financial options: the American Put option, American Cash-or-Nothing option and the American Asset-or-Nothing option.