Filtration Reduction and Completeness in Brownian Motion Models

In this paper we study an incomplete Brownian motion market and use filtration reduction to obtain a complete market, and hence a unique pricing measure. We then uplift the obtained 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 reduced information and a noise component. This allows us to give a precise meaning to the notion of irrelevant information in the context of filtration reduction