An extension of Arrow’s result on optimality of a stop loss contract

The optimal, from the cedent’s point of view, reinsurance treaties for a fixed reinsurer’s premium are derived. We assume that the cedent wants to minimize a convex risk measure, e.g. the variance, semi-variance, upper partial moment or mean absolute deviation. The reinsurer’s premium is calculated on the basis of the expectation and variance of his/her part of the total risk. The obtained results provide an extension of Arrow’s result on the optimality of a stop loss treaty.