Filtration reduction and completeness in Brownian motion models

This paper studies an incomplete Brownian motion market and uses filtration reduction to obtain a fictitious complete market with a unique pricing measure. We uplift this measure to the original market and study valuation and hedging via the uplifted measure. We show how a general market can be decomposed into a market corresponding to the reduced information plus a noise component. This allows us to give a precise meaning to the notion of irrelevant information in the context of a filtration reduction in an incomplete market.