Département de Mathématiques et de Génie Industriel, École Polytechnique, C.P. 6079, Succursale Centre-ville, Montréal, QC, H3C 3A7, Canada
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.
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.