A non-zero-sum reinsurance-investment game informed by alpha-maximin ambiguity-averse preferences

Yating Chen; Mi Chen; Xiang Hu; Yating Chen; Mi Chen; Xiang Hu

doi:10.3934/math.2026275

AIMS Mathematics

2026, Volume 11, Issue 3: 6649-6673. doi: 10.3934/math.2026275

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Research article

A non-zero-sum reinsurance-investment game informed by alpha-maximin ambiguity-averse preferences

1.
School of Mathematics and Statistics & Key Laboratory of Analytical Mathematics and Applications (Ministry of Education) & Fujian Provincial Key Laboratory of Statistics and Artificial Intelligence, Fujian Normal University, Fuzhou 350117, China
2.
School of Finance, Zhongnan University of Economics and Law, Nanhu Road, Wuhan 430073, China

Received: 01 December 2025 Revised: 03 February 2026 Accepted: 27 February 2026 Published: 16 March 2026
MSC : 62P05, 91B30

This paper investigates the optimal reinsurance and investment problem with delay in the framework of the non-zero-sum stochastic differential game, where the game is considered between two insurers characterized by similar ambiguity-averse preferences. Both insurers maximize their respective $ \alpha $-maxmin mean-variance criterion in the market. The criterion is time-inconsistent and we derive the equilibrium reinsurance-investment strategies and value functions by the extended HJB equations. Finally, some numerical examples and sensitivity analysis are presented to demonstrate the effects of model parameters on the equilibrium strategy. We find the delay factor and the various attitudes of decision-makers toward ambiguity have a great influence on the final strategy. Moreover, the insurer's investment behavior will be more aggressive the more intense its competition with other insurers and the greater its ambiguity-seeking.
- $ \alpha $-maxmin mean-variance criterion,
- non-zero-sum differential game,
- delay,
- time-consistent strategy,
- similar ambiguity-averse preferences
Citation: Yating Chen, Mi Chen, Xiang Hu. A non-zero-sum reinsurance-investment game informed by alpha-maximin ambiguity-averse preferences[J]. AIMS Mathematics, 2026, 11(3): 6649-6673. doi: 10.3934/math.2026275

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Abstract

This paper investigates the optimal reinsurance and investment problem with delay in the framework of the non-zero-sum stochastic differential game, where the game is considered between two insurers characterized by similar ambiguity-averse preferences. Both insurers maximize their respective $ \alpha $-maxmin mean-variance criterion in the market. The criterion is time-inconsistent and we derive the equilibrium reinsurance-investment strategies and value functions by the extended HJB equations. Finally, some numerical examples and sensitivity analysis are presented to demonstrate the effects of model parameters on the equilibrium strategy. We find the delay factor and the various attitudes of decision-makers toward ambiguity have a great influence on the final strategy. Moreover, the insurer's investment behavior will be more aggressive the more intense its competition with other insurers and the greater its ambiguity-seeking.

References

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