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We study the forward investment performance process (FIPP) in an incompletesemimartingale market model with closed and convex portfolio constraints, whenthe investor's risk preferences are of the power form. We provide necessary andsufficient conditions for the construction of such a performance process, andshow that it can be recovered as the unique solution of an infinite horizonquadratic backward stochastic differential equation (BSDE) with a nonmonotonedriver. In an integrated stochastic factor model, we relate the factorrepresentation of the BSDE solution to the smooth solution of an ill-posedpartial integro-differential Hamilton-Jacobi-Bellman (HJB) equation. We providean explicit construction of the BSDE solution for the class of time-monotoneFIPPs, generalizing existing results from Brownian to semimartingale marketmodels.

Power Forward Performance in Semimartingale Markets with Stochastic Integrated Factors