Drift operator in a viable expansion of information flow

A triplet (P,F,S) of a probability measure P, of an information flow F=(Ft)t∈R+, and of an F adapted asset process S, is a financial market model, only if it is viable. In this paper we are concerned with the preservation of the market viability, when the information flow F is replaced by a bigger one G=(Gt)t≥0 with Gt⊃Ft. Under the assumption of martingale representation property in (P,F), we prove a necessary and sufficient condition for all viable market in F remains viable in G.