Some Remarks on a Recent Paper by Borch

In his recent paper, "An Attempt to Determine the Optimum Amount of Stop Loss Reinsurance", presented to the XVIth International Congress of Actuaries, Dr. Karl Botch considers the problem of minimizing the variance of the total claims borne by the ceding insurer. Adopting this variance as a measure of risk, he considers as the most efficient reinsurance scheme that one which serves to minimize this variance. If x represents the amount of total claims with distribution function F (x), he considers a reinsurance scheme as a transformation of F (x). Attacking his problem from a different point of view, we restate and prove it for a set of transformations apparently wider than that which he allows.