Before revision:   In particular, we show that the optimality of the exit time of an interval (corresponding to the "cut-loss-or-stop-gain" strategy widely adopted in stock trading ) is endogenous for problems with convex distortion functions, including ones where distortion is absent.
After revision:  We also discuss economical interpretations of the results. In particular, we show that the optimality of the exit time of an interval (corresponding to the "cut-loss-or-stop-gain" strategy widely adopted in stock trading ) is endogenous for problems with convex distortion functions, including ones where distortion is absent.