Optimal reinsurance under variance related premium principles

In this paper, we investigate the optimal form of reinsurance when the insurer seeks to minimize the value at risk(VaR) or the conditional value at risk(CVaR) of his/her total risk exposure. In order to exclude the moral hazard from a reinsurance treaty, both the ceded and retained loss functions are constrained to be increasing. Under the additional assumption that the reinsurance premium is calculated by a variance related principle, we show that the layer reinsurance is always optimal over both the VaR and CVaR criteria. Finally, the variance and standard deviation premium principles are applied to illustrate how to derive the optimal deductible and the upper limit of layer reinsurance.