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2016, 6(1): 21-34. doi: 10.3934/naco.2016.6.21

## Optimal layer reinsurance on the maximization of the adjustment coefficient

 1 School of Mathematical Sciences, Institute of Finance and Statistics, Nanjing Normal University, Jiangsu 210023, China, China

Received  January 2015 Revised  December 2015 Published  January 2016

In this paper, we study the optimal retentions for an insurance company, 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 model. Moreover, we conclude that under the expected value principle there exists a special layer reinsurance strategy, i.e., excess of loss reinsurance strategy which is better than any other layer reinsurance strategies. 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.
Citation: Xuepeng Zhang, Zhibin Liang. Optimal layer reinsurance on the maximization of the adjustment coefficient. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 21-34. doi: 10.3934/naco.2016.6.21
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