Given a standard Brownian motion *B^{\mu}=(B_t^{\mu})_{0\le t\le T}* with drift *\mu \in \mathbb{R}* and letting *S_t^{\mu}=\max_{0\le s\le t}B_s^{\mu}* for *0\le t\le T*, we consider the optimal prediction problem: \[V=\inf_{0\le \tau \le T}\mathsf{E}(B_{\tau}^{\mu}-S_T^{\mu})^2\] where the infimum is taken over all stopping times *\tau* of *B^{\mu}*. Reducing the optimal prediction problem to... Show more

March 27, 2007

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