Optimal reinsurance-investment problem for two competitive or cooperative insurers under two investment patterns

Abstract

The optimal reinsurance-investment problem for two competitive or cooperative insurers is investigated. Each insurer transfers part of the claims risk via reinsurance and invests the surplus in a financial market consisting of one risk-free asset and two risky assets for increasing wealth. Both the aggregated claims of the two surplus processes and the aggregated jumps of the two risky assets are governed by a common Poisson process. We consider two relationships between the two insurers, i.e., competition and cooperation. In addition, we consider two kinds of investment patterns, called the concentration investment and the diversification investment. The objective of the each insurer is to choose the optimal reinsurance-investment strategy so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth. By the technique of stochastic control theory, the explicit optimal reinsurance-investment strategies and the optimal value functions are obtained in the two investment patterns for the competition case and the cooperation case, and some special cases. Finally, some numerical experiments are carried out to illustrate the effects of model parameters on the optimal strategies and the optimal value functions, which reveal some interesting phenomena and provide useful guidances for reinsurance and investment in reality.

Keywords:

• Reinsurance
• concentration investment
• diversification investment
• competition
• cooperation
• mean-variance criterion

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 62P05; 91B28; 93E20

Conflict of interest

The author declares that he has no conflicts of interest.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This research was supported by the Humanities and Social Sciences Project of the Ministry of Education of China under Grant number 21XJC910001 and the Project supported by Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2023-JC-YB-002).