We consider an optimal stopping problem recently posed by Shiryaev at the International Conference on Advanced Stochastic Optimization URLanized by the Steklov Institute of Mathematics in September 2012: \sup_{\tau\in\mathcal{T_{\eps,T}}EB_{\tau-\eps}, where }%DIFDELCMD < \eps %%% _{\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>%DIFDELCMD < \eps%%%  . We solve this problem by conditioning and then using the theory of reflected backward stochastic differential equations (RBSDEs). _{0,T}}EB_{(\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 consider _{\eps,T}}EB_{\tau-\eps}, where }%DIFDELCMD < \eps %%% the optimal problem \sup_{\tau\in\mathcal{T_{\eps,T}}E[i=1^n (\tau-\eps^i)^+^i], where T>0 } is a fixed time horizon, (\phi_t^i)_{0\leq t\leq T is progressively measurable with respect to the Brownian filtration, }\eps^i\in[0,T] is a constant, i=1,...o,n, and T_{\eps,T} is the set of stopping times that lie between a constant \eps %DIFDELCMD < \eps%%% \in[0,T] and T . 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}}EB_{(\tau-\eps)^+} recently posed by Shiryaev at the International Conference on Advanced Stochastic Optimization URLanized by the Steklov Institute of Mathematics in September 2012.}
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an optimal stopping problem recently posed by Shiryaev at the International Conference on Advanced Stochastic Optimization URLanized by the Steklov Institute of Mathematics in September 2012: \sup_{\tau\in\mathcal{T
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the optimal problem \sup_{\tau\in\mathcal{T
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strictly positive constant, B is a Brownian motion,
time horizon, (\phi_t^i)_{0\leq t\leq T
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^i\in[0,T] is a constant, i=1,...o,n,
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Brownian
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a constant
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and a fixed horizon T>
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\in[0,T] and T
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As a corollary, we provide the solution to the optimal stopping problem \sup_{\tau\in\mathcal{T