Non-zero-sum reinsurance and investment game under thinning dependence structure: mean–variance premium principle

Abstract

This paper considers a non-zero-sum stochastic differential reinsurance and investment game between two competitive insurers under the expected exponential utility. It is assumed that the surplus process of each insurer is characterized by a compound Poisson model and their claim businesses are correlated through thinning dependence structure. Each insurer can purchase proportional reinsurance and is allowed to invest in a risk-free asset and a risky asset. The insurers compete with each other and are concerned with the relative performance. By using the stochastic control technique, not only the existence and uniqueness of the optimal strategies are proved, but also the specific analyses for the constraint reinsurance strategies are provided. We find that (i) the thinning dependence structure has significant impact on optimal reinsurance strategies for both insurers and can help them reduce risks; (ii) the behavior of non-zero-sum game will reduce the proportion of purchasing reinsurance for each insurer.

Keywords:

• Thinning dependence
• non-zero-sum game
• reinsurance and investment
• mean–variance premium

Acknowledgments

We would like to thank the anonymous reviewers and the Editor for their constructive comments and suggestions on an earlier version of this paper, which led to a considerable improvement of the presentation of the work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China (Grant Nos. 12071224 and 12101299), Natural Science Foundation of Jiangsu Province (Grant No. BK20210668), and the Philosophy and Social Science Foundation for Colleges and Universities of Jiangsu Province (Grant No. 2020SJA0261).