Copyright © 2011 Mario Lefebvre. This is an open access article distributed under the Creative Commons Attribution License,, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a controlled one-dimensional standard Brownian motion starting from . The problem of optimally controlling until for the first time is solved explicitly in a particular case. The maximal value that the instantaneous reward given for survival in can take is determined.