Optimal layer reinsurance on the maximization of the adjustment coefficient

Abstract

In this paper, we study the optimalretentions for an insurance company, which intends to transferrisk by means of a layer reinsurance treaty. Under the criterion ofmaximizing the adjustment coefficient, the closed form expressionsof the optimal results are obtained for the Brownian motion riskmodel as well as the compound Poisson risk model. Moreover, weconclude that under the expected value principle there exists a special layer reinsurance strategy, i.e., excess of loss reinsurancestrategy which is better than any other layer reinsurancestrategies. Whereas, under the variance premium principle, the pure excess of loss reinsurance is not the optimal layer reinsurance strategy any longer. Some numerical examples are presented to show the impacts of the parameters as well as the premium principles on the optimal results.