Optimal Reinsurance Under The Distortion Risk Measure

Recently the optimal reinsurance strategy concerning an insurer's risk attitude andthe reinsurance premium principles is an interesting topic. This thesis concerns theoptimal reinsurance problems with the insurer's risk measured by the distortion riskmeasure.Under a reasonable assumption that both the ceded loss and the retained loss areincreasing with the initial loss, explicit solutions of the optimal reinsurance problemsare derived when the reinsurance premium calculated by a general principle includingexpected premium principle and Wang's premium principle as its special cases. Withthe help of a new method, one can explain the optimal reinsurance treaty in the view ofa balance between the insurer's risk measure and the reinsurance premium principle.Some studies found the truncated stop loss strategy, where the ceded loss is notincreasing with the initial loss, is optimal. As a complement, we relaxed the restric-tion on ceded loss and only assume the retained loss is an increasing function of theinitial loss. When the insurer's risk is measured by the distortion risk measure and thereinsurance premium is calculated by expected premium principle, explicit solution ofthe optimal reinsurance strategy is obtained. The optimal strategies for some specialdistortion risk measures, such as value-at-risk (VaR) and tail value-at-risk (TVaR) arealso investigated.