Optimal investment-reinsurance problems with common shock dependent risks under two kinds of premium principles

This paper considers the optimal investment-reinsurance strategy in a risk model with two dependent classes of insurance business under two kinds of premium principles, where the two claim number processes are correlated through a common shock component. Under the criterion of maximizing the expected exponential utility with the expected value premium principle and the variance premium principle, we use the stochastic optimal control theory to derive the optimal strategy and the value function for the compound Poisson risk model as well as for the Brownian motion diffusion risk model. In particular, we find that the optimal investment strategy on the risky asset is independent to the reinsurance strategy and the reinsurance strategy for the compound Poisson risk model are very different from those for the diffusion model under both two kinds of premium principles, but the investment strategies are the same in this two risk models. Finally, numerical examples are presented to show the impact of model parameters in the optimal strategies.