In this paper, we consider the problem of optimal reinsurance design, whenthe risk is measured by a distortion risk measure and the premium is given by adistortion risk premium. First, we show how the optimal reinsurance design forthe ceding company, the reinsurance company and the social planner can beformulated in the same way. Second, by introducing the marginal indemnificationfunctions, we characterize the optimal reinsurance contracts. We show that, foran optimal policy, the associated marginal indemnification function only takesthe values zero and one. We will see how the roles of the market preferencesand premiums and that of the total risk are separated.
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