A Stackelberg reinsurance-investment game on asset-liability management under CEV model

Liangli Chen; Zhijian Qiu; Lu Li; Liangli Chen; Zhijian Qiu; Lu Li

doi:10.3934/jimo.2026115

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 7: 3151-3174. doi: 10.3934/jimo.2026115

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Research article

A Stackelberg reinsurance-investment game on asset-liability management under CEV model

1.
School of Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, China
2.
School of Mathematics and Physics, Yibin University, Yinbin, 644000, China

Received: 23 January 2026 Revised: 10 April 2026 Accepted: 29 May 2026 Published: 10 June 2026
91A23, 93E20

This paper investigates the optimal reinsurance-investment problem within the framework of a Stackelberg differential game. Under the constant elasticity of variance (CEV) model, a Stackelberg game model for investment-reinsurance asset-liability management between an insurer and a reinsurer is innovatively constructed. The two players are the insurer (follower) and the reinsurer (leader): The insurer aims to determine the optimal reinsurance and investment strategies, and the reinsurer seeks to formulate the optimal premium pricing and investment strategies. Both parties can allocate a risk-free asset and a risky asset whose price processes follow the CEV model, and both are exposed to uncontrollable external liabilities. To address the time–inconsistency issue in the game, the mean-variance criterion is adopted, formulating the optimization problems of both players as a nested game and deriving the corresponding extended Hamilton–Jacobi–Bellman equations. Based on this analytical framework, a verification theorem is formulated, which explicitly derives equilibrium reinsurance- investment strategies as well as the corresponding value functions for both the insurer and the reinsurer. Finally, numerical examples are provided to illustrate the rightness of our conclusions.
- reinsurance,
- asset-liability,
- Stackelberg game,
- HJB equation,
- investment-reinsurance strategy
Citation: Liangli Chen, Zhijian Qiu, Lu Li. A Stackelberg reinsurance-investment game on asset-liability management under CEV model[J]. Journal of Industrial and Management Optimization, 2026, 22(7): 3151-3174. doi: 10.3934/jimo.2026115

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Abstract

This paper investigates the optimal reinsurance-investment problem within the framework of a Stackelberg differential game. Under the constant elasticity of variance (CEV) model, a Stackelberg game model for investment-reinsurance asset-liability management between an insurer and a reinsurer is innovatively constructed. The two players are the insurer (follower) and the reinsurer (leader): The insurer aims to determine the optimal reinsurance and investment strategies, and the reinsurer seeks to formulate the optimal premium pricing and investment strategies. Both parties can allocate a risk-free asset and a risky asset whose price processes follow the CEV model, and both are exposed to uncontrollable external liabilities. To address the time–inconsistency issue in the game, the mean-variance criterion is adopted, formulating the optimization problems of both players as a nested game and deriving the corresponding extended Hamilton–Jacobi–Bellman equations. Based on this analytical framework, a verification theorem is formulated, which explicitly derives equilibrium reinsurance- investment strategies as well as the corresponding value functions for both the insurer and the reinsurer. Finally, numerical examples are provided to illustrate the rightness of our conclusions.

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