  In this paper, we introduce an extension of a Brownian bridge with a random
length by including uncertainty also in the pinning level of the bridge. The
main result of this work is that unlike for deterministic pinning point, the
bridge process fails to be Markovian if the pining point distribution is
absolutely continuous with respect to the Lebesgue measure. Further results
include the derivation of formulae to calculate the conditional expectation of
various functions of the random pinning time, the random pinning location, and
the future value of the Brownian bridge, given an observation of the underlying
process. For the specific case that the pining point has a two-point
distribution, we state further properties of the Brownian bridge, e.g., the
right continuity of its natural filtration and its semi-martingale
decomposition. The newly introduced process can be used to model the flow of
information about the behaviour of a gas storage contract holder; concerning
whether to inject or withdraw gas at some random future time.
