Date of Award
Master of Science
Richard H. Stockbridge
Eric S. Key, Chao Zhu
American Option, Geometric Brownian Motion, Integral Representation for Excessive Function, Optimal Investment Problem, Optimal Stopping Problem, Riesz Representation
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.
Schuster, Markus, "On the Riesz Representation for Optimal Stopping Problems" (2015). Theses and Dissertations. 838.