This talk is concerned with the optimal investment and risk control problem for an insurer subject to a stochastic economic factor in a Lévy market. In our mathematical model, a riskless bond and a risky asset are assumed to rely on a stochastic economic factor which is described by a Lévy stochastic differential equation (SDE). The risk process is described by a new “jump diffusion” SDE depending on the stochastic economic factor and is negatively correlated with capital gains in the financial market. Using expected utility maximization, we characterize the optimal strategies of investment and risk control under the logarithmic utility function and the power utility function, respectively. With the logarithmic utility assumption, we use the classical optimization method to obtain the optimal strategy. However, for the power utility function, we apply dynamic programming principle to derive the Hamilton–Jacobi–Bellman (HJB) equation, and analyze its solution in order to obtain the optimal strategy. We also show the verification theorem. Finally, to study the impact of the market parameters on the optimal strategies, we conduct a numerical analysis.