Optimal portfolio and reinsurance with two differential risky assets

This article considers the optimal reinsurance-portfolio problem that the insurer invests in two related risky assets described by different types: constant elasticity of variance model and jump-diffusion process model, besides a risk-free asset. There is a correlation between the diffusion processes of the two models. Meanwhile, the company purchases proportional reinsurance. Specially, assume the claim process follows a Levy process and the reinsurance's premium principle has not to be certain. Then based on stochastic control theory, a novel form of the optimal value function for solving the Hamilton-Jacobi-Bellman equation is constructed. Finally, the expressions of the optimal results are obtained under maximizing the expected exponential utility of terminal wealth. In addition, we listed several examples of the common premium principles. Numerical simulations are supplied for sensitivity analysis of parameters.