Robust equilibrium reinsurance and investment strategy for the insurer and reinsurer under weighted mean-variance criterion

Yiming Su; Haiyan Liu; Mi Chen; Yiming Su; Haiyan Liu; Mi Chen

doi:10.3934/era.2023323

Electronic Research Archive

2023, Volume 31, Issue 10: 6384-6411. doi: 10.3934/era.2023323

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Research article

Robust equilibrium reinsurance and investment strategy for the insurer and reinsurer under weighted mean-variance criterion

1.
School of Mathematics and Statistics & Fujian Key Laboratory of Analytical Mathematics and Applications, Fujian Normal University, Fuzhou 350117, China
2.
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

Received: 05 August 2023 Revised: 10 September 2023 Accepted: 20 September 2023 Published: 25 September 2023

This paper investigates the time-consistent robust optimal reinsurance problem for the insurer and reinsurer under weighted objective criteria. The joint objective criterion is obtained by weighting the mean-variance objectives of both the insurer and reinsurer. Specifically, we assume that the net claim process is approximated by a diffusion model, and the insurer can purchase proportional reinsurance from the reinsurer. The insurer adopts the loss-dependent premium principle considering historical claims, while the reinsurance contract still uses the expected premium principle due to information asymmetry. Both the insurer and reinsurer can invest in risk-free assets and risky assets, where the risky asset price is described by the constant elasticity of variance model. Additionally, the ambiguity-averse insurer and ambiguity-averse reinsurer worry about the uncertainty of parameter estimation in the model, therefore, we obtain a robust optimization objective through the robust control method. By solving the corresponding extended Hamilton-Jacobi-Bellman equation, we derive the time-consistent robust equilibrium reinsurance and investment strategy and corresponding value function. Finally, we examined the impact of various parameters on the robust equilibrium strategy through numerical examples.
- the insurer and reinsurer,
- loss-dependent premium principle,
- constant elasticity of variance model,
- weighted mean-variance criterion,
- ambiguity aversion
Citation: Yiming Su, Haiyan Liu, Mi Chen. Robust equilibrium reinsurance and investment strategy for the insurer and reinsurer under weighted mean-variance criterion[J]. Electronic Research Archive, 2023, 31(10): 6384-6411. doi: 10.3934/era.2023323

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Abstract

This paper investigates the time-consistent robust optimal reinsurance problem for the insurer and reinsurer under weighted objective criteria. The joint objective criterion is obtained by weighting the mean-variance objectives of both the insurer and reinsurer. Specifically, we assume that the net claim process is approximated by a diffusion model, and the insurer can purchase proportional reinsurance from the reinsurer. The insurer adopts the loss-dependent premium principle considering historical claims, while the reinsurance contract still uses the expected premium principle due to information asymmetry. Both the insurer and reinsurer can invest in risk-free assets and risky assets, where the risky asset price is described by the constant elasticity of variance model. Additionally, the ambiguity-averse insurer and ambiguity-averse reinsurer worry about the uncertainty of parameter estimation in the model, therefore, we obtain a robust optimization objective through the robust control method. By solving the corresponding extended Hamilton-Jacobi-Bellman equation, we derive the time-consistent robust equilibrium reinsurance and investment strategy and corresponding value function. Finally, we examined the impact of various parameters on the robust equilibrium strategy through numerical examples.

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