Predicting the Last Zero of Brownian Motion with Drift

Given a standard Brownian motion B^{\mu}=(B_t^{\mu})_{0\le t\le T} with drift \mu \in IR and letting g denote the last zero of B^{\mu} before T, we consider the optimal prediction problem V_*=\inf_{0\le \tau \le T}\mathsf {E}\:|\:g-\tau | where the infimum is taken over all stopping times \tau of B^{\mu}. Reducing the... Show more