Optimal Layer Reinsurance To Maximize The Adjustment Coefficient

In this article, we study the optimal retentions for an insurance com-pany, which intends to transfer risk by means of a layer reinsurance treaty. Under the criterion of maximizing the adjustment coefficient, the closed form expressions of the optimal results are obtained for the Brownian motion risk model as well as the compound Poisson risk mod-el. Moreover, we conclude that under the expected value principle there exists a special layer reinsurance strategy, i.e., excess of loss reinsur-ance strategy which is better than any other layer reinsurance strategy. Whereas, under the variance premium principle, the optimal results will be very different. Some numerical examples are presented to show the impacts of the parameters as well as the premium principles on the opti-mal results.