Abstract
In this article, we study the optimal insurance-reinsurance problem from the perspectives of both insurers and reinsurers. Namely, we study the optimal insurance-reinsurance treaties by minimizing the convex combination of the risk measurements of the insurer and the reinsurer, and taking into account the reinsurer’s default risk. We assume that the risks of the insurer and the reinsurer, as well as the insurance premium and the reinsurance premium, are calculated by some distortion risk measures with different distortion functions. Optimal insurance-reinsurance treaties are provided. Finally, an illustrating numerical example is given.
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