  The paper generalizes the construction by stochastic flows of consistent
utility processes introduced by M. Mrad and N. El Karoui in (2010). The
utilities random fields are defined from a general class of processes denoted
by $\GX$. Making minimal assumptions and convex constraints on test-processes,
we construct by composing two stochastic flows of homeomorphisms, all the
consistent stochastic utilities whose the optimal-benchmark process is given,
strictly increasing in its initial condition. Proofs are essentially based on
stochastic change of variables techniques.
