In this paper we consider the problem of optimal reinsurance design for general distortion risk measures and premiums … solutions always have a multilayer structure. In addition we will see that for particular risk measures VaR and CVaR the optimal …

This paper unifies the work on multiple reinsurers, distortion risk measures, premium budgets,and heterogeneous beliefs …. An insurer minimizes a distortion risk measure, while seekingreinsurance with finitely many reinsurers. The reinsurers … examples withthe Conditional Value-at-Risk illustrate our results …

This paper presents a random risk measure, named as the random distortionrisk measure. The random distortion risk … measure is a generalization of thetraditional deterministic distortion risk measure by randomizing thedeterministic distortion … function and the risk distribution respectively,where a stochastic distortion is introduced to randomize the distortionfunction …