  Motivation for this paper is to understand the impact of information on asset
price bubbles and perceived arbitrage opportunities. This boils down to study
optional projections of $\mathbb{G}$-adapted strict local martingales into a
smaller filtration $\mathbb{F}$ under equivalent martingale measures. We give
some general results as well as analyze in details two specific examples given
by the inverse three dimensional Bessel process and a class of stochastic
volatility models.
