Pareto-optima Reinsurance Strategy Under General Premium Principles

Reinsurance is the transfer of risk from a direct insurer, the insurer, to a second insurance carrier, the reinsurer. It is necessary to transfer his risk through reinsurance for an insurer, especially, when he faces the huge risk. One of the key problems is the optimal reinsurance. How to choose the optimal reinsurance method becomes the urgent problem that the insurer needs to solve.Optimal reinsurance from an insurer's point of view or from a reinsurer's point of view has been studied for a long time in the literatures. However, as two parties of a reinsurance contract, there is a conflict of interests between the insurer and the reinsurer. An optimal reinsurance policy from one party's point of view may not be optimal for another party and it might be unacceptable for another party.Therefore, in this paper we study forms of Pareto optimal reinsurance policies which can be determined by minimizing the convex combination of the VaRs of the two parties. We derive the optimal reinsurance forms within different classes of ceded loss functions under the criterion of VaR when the reinsurance premium principles satisfy risk loading and stop-loss ordering preserving. When the ceded loss functions are increasing and convex, we determine the optimal reinsurance forms using the geometric approach. Then we demonstrate the applicability of our results by resorting to the Dutch premium principle and the Wang's premium principle and derive the optimal parameters. Also we assume that the ceded loss functions are in the class of increasing and concave and the premium is calculated by the expected value premium principle. We derive the optimal reinsurance forms and optimal parameters.