Given a deterministically time-changed Brownian motion Z starting from 1, whose time-change V(t) satisfies V(t) t for all t 0, we perform an explicit construction of a process X which is Brownian motion in its own filtration and that hits zero for the first time at V(τ), where τ:= inf {t 0:...

Given a Markovian Brownian martingale Z, we build a process X which is a martingale in its own filtration and satisfies X1=Z1. We call X a dynamic bridge, because its terminal value Z1 is not known in advance. We compute its semimartingale decomposition explicitly under both its own filtration...