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A reinsurance contract should address the conflicting interests of theinsurer and reinsurer. Most of existing optimal reinsurance contracts onlyconsiders the interests of one party. This article combines the proportionaland stop-loss reinsurance contracts and introduces a new reinsurance contractcalled proportional-stop-loss reinsurance. Using the balanced loss function,unknown parameters of the proportional-stop-loss reinsurance have beenestimated such that the expected surplus for both the insurer and reinsurer aremaximized. Several characteristics for the new reinsurance are provided.

An Optimal Combination of Proportional and Stop-Loss Reinsurance Contracts From Insurer's and Reinsurer's Viewpoints