Time-inconsistent reinsurance and investment optimization problem with delay under random risk aversion
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| Format: | Preprint |
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2025
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| _version_ | 1866914271719325696 |
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| author | Kang, Jian-hao Gou, Zhun Huang, Nan-jing |
| author_facet | Kang, Jian-hao Gou, Zhun Huang, Nan-jing |
| contents | This paper considers a newly delayed reinsurance and investment optimization problem incorporating random risk aversion, in which an insurer pursues maximization of the expected certainty equivalent of her/his terminal wealth and the cumulative delayed information of the wealth over a period. Specially, the insurer's surplus dynamics are approximated using a drifted Brownian motion, while the financial market is described by the constant elasticity of variance (CEV) model. Moreover, the performance-linked capital flow feature is incorporated and the wealth process is formulated via a stochastic delay differential equation (SDDE). By adopting a game-theoretic approach, a verification theorem with rigorous proofs is established to capture the equilibrium reinsurance and investment strategy along with the equilibrium value function. Furthermore, analytical or semi-analytical equilibrium reinsurance and investment strategies, together with their equilibrium value functions, are obtained under the CEV model for the exponential utility and derived under the Black-Scholes model for both exponential and power utilities. Finally, several numerical experiments are conducted to analyze the behavioral characteristics of the freshly-derived equilibrium reinsurance and investment strategy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_15506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-inconsistent reinsurance and investment optimization problem with delay under random risk aversion Kang, Jian-hao Gou, Zhun Huang, Nan-jing Optimization and Control This paper considers a newly delayed reinsurance and investment optimization problem incorporating random risk aversion, in which an insurer pursues maximization of the expected certainty equivalent of her/his terminal wealth and the cumulative delayed information of the wealth over a period. Specially, the insurer's surplus dynamics are approximated using a drifted Brownian motion, while the financial market is described by the constant elasticity of variance (CEV) model. Moreover, the performance-linked capital flow feature is incorporated and the wealth process is formulated via a stochastic delay differential equation (SDDE). By adopting a game-theoretic approach, a verification theorem with rigorous proofs is established to capture the equilibrium reinsurance and investment strategy along with the equilibrium value function. Furthermore, analytical or semi-analytical equilibrium reinsurance and investment strategies, together with their equilibrium value functions, are obtained under the CEV model for the exponential utility and derived under the Black-Scholes model for both exponential and power utilities. Finally, several numerical experiments are conducted to analyze the behavioral characteristics of the freshly-derived equilibrium reinsurance and investment strategy. |
| title | Time-inconsistent reinsurance and investment optimization problem with delay under random risk aversion |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2509.15506 |