Optional projection under equivalent local martingale measures

We study optional projections of \({\mathbb{G}}\)-adapted strict local martingales on a smaller filtration \({\mathbb{F}}\) under changes of equivalent martingale measures. General results are provided as well as a detailed analysis of two specific examples given by the inverse Bessel process and a class of stochastic volatility models. This analysis contributes to clarify the absence of arbitrage opportunities of market models under restricted information.