On Optimal Reinsurance Policy with Distortion Risk Measures and Premiums
17 Pages Posted: 13 Jun 2014 Last revised: 16 Jul 2014
Date Written: June 11, 2014
In this paper, we consider the problem of optimal reinsurance design, when the risk is measured by a distortion risk measure and the premium is given by a distortion risk premium. First, we show how the optimal reinsurance design for the ceding company, the reinsurance company and the social planner can be formulated in the same way. Second, by introducing the “marginal indemnification functions”, we characterize the optimal reinsurance contracts. We show that, for an optimal policy, the associated marginal indemnification function only takes the values zero and one. We will see how the roles of the market preferences and premiums and that of the total risk are separated.
Keywords: Distortion risk and premium, optimal reinsurance design
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