Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles

- Optimal reinsurance strategy is discussed in this paper.
- We assume that both the ceded loss and the retained loss are increasing functions.
- The insurer's risk is measured by the distortion risk measure.
- The reinsurance premium principle includes some widely used premium principles.
- Explicit solutions of the optimal reinsurance strategy are obtained.

Recently the optimal reinsurance strategy concerning the insurer's risk attitude and the reinsurance premium principle has been an interesting topic. This paper discusses the optimal reinsurance problem with the insurer's risk measured by distortion risk measure and the reinsurance premium calculated by a general principle including expected premium principle and Wang's premium principle as its special cases. Explicit solutions of the optimal reinsurance strategy are obtained under the assumption that both the ceded loss and the retained loss are increasing with the initial loss. We present a new method for discussing the optimal problem. Based on our method, one can explain the optimal reinsurance treaty in the view of a balance between the insurer's risk measure and the reinsurance premium principle.