Optimal investment and reinsurance strategies for an insurer with stochastic economic factor

This work considers optimal investment and reinsurance strategies for an insurer with sto-chastic economic factor. In our mathematical model, a risk-free asset and a risky asset are assumed to rely on a stochastic economic factor which is described by a diffusion process. We generalize the claim process to a compound Poisson process with the stochastic eco-nomic factor. Using expected utility maximization, we characterize the optimal strategy of investment-reinsurance under the power utility function. We use dynamic programming principle to derive the Hamilton-Jacobi-Bellman (HJB) equation. Then, by analysing the solution of the HJB equation, the optimal investment-reinsurance strategy is obtained and given in the verification theorem. Finally, sensitivity analysis is given to show the economic behavior of the optimal investment and reinsurance strategies.