Before revision: T}}EB_{\tau-\eps}, where } _{\eps,T}}E[i=1^n (\tau-\eps^i)^+^i], where T>0 } is a fixed strictly positive constant, B is a Brownian motion, is progressively measurable with respect to the Brownian filtration, }\eps and T_{\eps,T} is the set of Brownian stopping times that lie between  \eps and a fixed horizon T>  . We solve this problem by conditioning and then using the theory of reflected backward stochastic differential equations (RBSDEs).
After revision: T}}EB_{\tau-\eps}, where } the optimal problem \sup_{\tau\in\mathcal{T_{\eps,T}}E[i=1^n (\tau-\eps^i)^+^i], where T>0 } is a fixed strictly positive constant, B is a Brownian motion, is progressively measurable with respect to the Brownian filtration, }\eps and T_{\eps,T} is the set of Brownian stopping times that lie between \eps and a fixed horizon T> . We solve this problem by conditioning and then using the theory of reflected backward stochastic differential equations (RBSDEs).