  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 construction of such a performance process, and
show that it can be recovered as the unique solution of an infinite horizon
quadratic backward stochastic differential equation (BSDE) with a nonmonotone
driver. In an integrated stochastic factor model, we relate the factor
representation of the BSDE solution to the smooth solution of an ill-posed
partial integro-differential Hamilton-Jacobi-Bellman (HJB) equation. We provide
an explicit construction of the BSDE solution for the class of time-monotone
FIPPs, generalizing existing results from Brownian to semimartingale market
models.
