  We consider an auction type equilibrium model with an insider in line with
the one originally introduced by Kyle in 1985 and then extended to the
continuous time setting by Back in 1992. The novelty introduced with this paper
is that we deal with a general price functional depending on the whole past of
the aggregate demand, i.e. we work with path-dependency. By using the
functional It\^o calculus, we provide necessary and sufficient conditions for
the existence of an equilibrium. Furthermore, we consider both the cases of a
risk-neutral and a risk-averse insider.
