Before revision:  Inspired by the study in \mbox{%DIFAUXCMD EKK1989 on reflected follower problems, we relate the optimal dividend problem with capital injections to an optimal stopping problem for a drifted Brownian motion that is absorbed at zero .
After revision:  Inspired by the study of El Karoui and Karatzas (1989) on reflected follower problems, we relate the optimal dividend problem with capital injections to an optimal stopping problem for a drifted Brownian motion that is absorbed at zero .