  We study the forward investment performance process (FIPP) in an incomplete
semimartingale market model with closed and convex portfolio constraints, when
the investor's risk preferences are of the power form. We provide necessary and
sufficient conditions for the existence of such FIPP. In a semimartingale
factor model, we show that the FIPP can be recovered as a triplet of processes
which admit an integral representation with respect to semimartingales. Using
an integrated stochastic factor model, we relate the factor representation of
the triplet of processes to the smooth solution of an ill-posed partial
integro-differential Hamilton-Jacobi-Bellman (HJB) equation. We develop
explicit constructions for the class of time-monotone FIPPs, generalizing
existing results from Brownian to semimartingale market models.
