Reinsurance Optimal Design with Distortion Risk Measures and Risk Premiums
20 Pages Posted: 6 Jun 2015
Date Written: June 4, 2015
In this paper we consider the problem of optimal reinsurance design for general distortion risk measures and premiums. In the first part of the paper, we find the Lagrangian dual of the primal optimal reinsurance problem and show the strong duality holds. Therefore we characterize the optimal reinsurance policies by solving the dual problem and we will see that the solutions always have a multilayer structure. In addition we will see that for particular risk measures VaR and CVaR the optimal solutions are stop-loss policies. In the second part we focus our attention to reinsurance policies that are usually traded in the market, namely stop-loss, stop-loss after quota share and quota-share after stop-loss. We show how by one can find the optimal retentions by checking Karush-Kuhn-Tucker conditions. At the end, we study the particular cases VaR or CVaR.
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