Optimal investment and risk control for an insurer with stochastic factor

We study an optimal investment and risk control problem for an insurer under stochastic factor. The insurer allocates his wealth across a riskless bond and a risky asset whose drift and volatility depend on a factor process. The risk process is modeled by a jump-diffusion with state-dependent jump measure. By maximizing the expected power utility of the terminal wealth, we characterize the optimal strategy of investment and risk control, analyze classical solutions of HJB PDE and prove the verification theorem.