 We solve this problem by conditioning and then using the theory of  reflected backward stochastic differential equations (RBSDEs). As a corollary, we provide the solution to the optimal stopping problem \sup_{\tau\in\mathcal{T_{0,T}}\mathbb{E}B_{(\tau-\eps)^+} recently posed by Shiryaev at the International Conference on Advanced Stochastic Optimization URLanized by the Steklov Institute of Mathematics in September 2012.
<meaning-changed>  We solve this problem by conditioning and then using the theory of  reflected backward stochastic differential equations (RBSDEs). As a corollary, we provide the solution to the optimal stopping problem \sup_{\tau\in\mathcal{T_{0,T}}\mathbb{E}B_{(\tau-\eps)^+} recently posed by Shiryaev at the International Conference on Advanced Stochastic Optimization URLanized by the Steklov Institute of Mathematics in September 2012.
 We solve this problem by conditioning and then using the theory of reflected backward stochastic differential equations _{0,T}}\mathbb{E}B_{(\tau-\eps)^+} recently posed by Shiryaev at the International Conference on Advanced Stochastic Optimization URLanized by the Steklov Institute of Mathematics in September 2012.