Optimal reinsurance contract and investment strategy for multiple competitive-cooperative insurers and a reinsurer

IF 1.9 3区工程技术 Q3 MANAGEMENT

IMA Journal of Management Mathematics Pub Date : 2023-07-15 DOI:10.1093/imaman/dpad012

Tao Wang, Zhiping Chen, Peng Yang

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Abstract

In this article, we consider a reinsurance contract design by taking into account the joint interests of multiple insurers and a reinsurer. The reinsurance contract consists of optimal reinsurance strategies and reinsurance prices. The former are chosen by the competitive-cooperative insurers and the latter are determined by a reinsurer. Both insurers and the reinsurer can invest in the common risk-free asset and one different risky asset. The optimal time-consistent reinsurance-investment strategies of the insurers and the optimal reinsurance prices and investment strategy of the reinsurer are derived analytically. Numerical experiments are carried out to illustrate the influences of model parameters on the optimal reinsurance contract and optimal investment strategies. We find that the establishment of the reinsurance contract is affected by the correlation between the claim sizes of insurers as well as that of claim numbers. The results reveal that competition and cooperation will lead to a decrease and increase of the reinsurance price, respectively, showing the importance of opting for cooperation among insurers. Both competition and cooperation are beneficial to insurers, especially for those with high risk aversion.

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多家竞争性合作保险公司和再保险人的最优再保险合同和投资策略

在本文中，我们通过考虑多个保险人和一个再保险人的共同利益来考虑再保险合同设计。再保险合同包括最优再保险策略和再保险价格。前者由有竞争力的合作保险公司选择，后者由再保险人决定。保险公司和再保险人都可以投资于共同的无风险资产和一种不同的风险资产。分析推导了保险人的最优时间一致再保险投资策略以及再保险人的最优再保险价格和投资策略。通过数值实验说明了模型参数对最优再保险合同和最优投资策略的影响。我们发现，再保险合同的成立受到保险公司索赔规模与索赔数量之间相关性的影响。研究结果表明，竞争和合作将分别导致再保险价格的下降和上升，表明了保险公司选择合作的重要性。竞争和合作对保险公司都是有利的，尤其是对那些风险厌恶度高的保险公司。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IMA Journal of Management Mathematics OPERATIONS RESEARCH & MANAGEMENT SCIENCE-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The mission of this quarterly journal is to publish mathematical research of the highest quality, impact and relevance that can be directly utilised or have demonstrable potential to be employed by managers in profit, not-for-profit, third party and governmental/public organisations to improve their practices. Thus the research must be quantitative and of the highest quality if it is to be published in the journal. Furthermore, the outcome of the research must be ultimately useful for managers. The journal also publishes novel meta-analyses of the literature, reviews of the "state-of-the art" in a manner that provides new insight, and genuine applications of mathematics to real-world problems in the form of case studies. The journal welcomes papers dealing with topics in Operational Research and Management Science, Operations Management, Decision Sciences, Transportation Science, Marketing Science, Analytics, and Financial and Risk Modelling.