Continuous-time optimal reinsurance strategy with nontrivial curved structures

This work uses different classes of premium principles (including the expected value premium principle, the variance premium principle and the exponential premium principle) as well as optimal reinsurance problems to minimize the probability of ruin and maximize the expected utility in both a diffusion insurance risk model and a compound Poisson insurance risk model. The optimal reinsurance strategy with a nontrivial structure and its respective optimal value function are obtained. Specifically, the optimal reinsurance strategy has a curved form, which is distinguished from the conventional proportional and excess-of-loss reinsurance strategies. Numerical analyses are provided to illustrate the behaviors of the optimal reinsurance strategies under different objective criteria and different insurance risk processes.