Summary: We extend our earlier work on the jump-diffusion risk-sensitive asset management problem in a factor model [M. Davis and S. Lleo, SIAM J. Financ. Math. 2, 22–54 (2011; Zbl 1217.91168)] by allowing jumps in both the factor process and the asset prices, as well as stochastic volatility and investment constraints. In this case, the Hamilton-Jacobi-Bellman (HJB) equation is a partial integro-differential equation (PIDE). We are able to show that finding a viscosity solution to this PIDE is equivalent to finding a viscosity solution to a related PDE, for which classical results give uniqueness. With this in hand, a policy improvement argument and classical results on parabolic PDEs show that the HJB PIDE admits a unique smooth solution. The optimal investment strategy is given by the feedback control that minimizes the Hamiltonian function appearing in the HJB PIDE.