Power Forward Performance in Semimartingale Markets with Stochastic Integrated Factors

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.