Optimal layer reinsurance on the  maximization of the adjustment coefficient

Xuepeng  Zhang; Zhibin  Liang

doi:10.3934/naco.2016.6.21

Article Contents

2016, Volume 6, Issue 1: 21-34. Doi: 10.3934/naco.2016.6.21

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Optimal layer reinsurance on the maximization of the adjustment coefficient

Xuepeng Zhang^1, and
Zhibin Liang^1,

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

Received: January 2015

Revised: December 2015

Published: January 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 62P05; Secondary: 91B30.

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