Optimal investment and reinsurance for the insurer and reinsurer with the joint exponential utility
In this paper, we consider the problem of optimal investment-reinsurance for the insurer and reinsurer under the stochastic volatility model. The surplus process of the insurer is described by a diffusion model. The insurer can purchase proportional reinsurance from the reinsurer and the premium cha...
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241672 |
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| author | Wuyuan Jiang Zechao Miao Jun Liu |
| author_facet | Wuyuan Jiang Zechao Miao Jun Liu |
| author_sort | Wuyuan Jiang |
| collection | DOAJ |
| description | In this paper, we consider the problem of optimal investment-reinsurance for the insurer and reinsurer under the stochastic volatility model. The surplus process of the insurer is described by a diffusion model. The insurer can purchase proportional reinsurance from the reinsurer and the premium charged by the insurer and reinsurer follows the variance principle. Both the insurer and reinsurer are allowed to invest in risk-free assets and risky assets, and the market price of risk depends on a Markovian, affine-form, and square-root stochastic factor process. Our goal is to maximize the joint exponential utility of the terminal wealth of the insurer, and reinsurer over a certain period of time. By solving the HJB equation, we obtain the optimal investment-reinsurance strategies, and present the proof of the verification theorem. Finally, we demonstrate a numerical analysis, and the economic implications of our findings are illustrated. |
| format | Article |
| id | doaj-art-9028bdb6a97340d5b55478c3911593f4 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-9028bdb6a97340d5b55478c3911593f42025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912351813521710.3934/math.20241672Optimal investment and reinsurance for the insurer and reinsurer with the joint exponential utilityWuyuan Jiang0Zechao Miao1Jun Liu2Department of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, ChinaDepartment of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, ChinaDepartment of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, ChinaIn this paper, we consider the problem of optimal investment-reinsurance for the insurer and reinsurer under the stochastic volatility model. The surplus process of the insurer is described by a diffusion model. The insurer can purchase proportional reinsurance from the reinsurer and the premium charged by the insurer and reinsurer follows the variance principle. Both the insurer and reinsurer are allowed to invest in risk-free assets and risky assets, and the market price of risk depends on a Markovian, affine-form, and square-root stochastic factor process. Our goal is to maximize the joint exponential utility of the terminal wealth of the insurer, and reinsurer over a certain period of time. By solving the HJB equation, we obtain the optimal investment-reinsurance strategies, and present the proof of the verification theorem. Finally, we demonstrate a numerical analysis, and the economic implications of our findings are illustrated.https://www.aimspress.com/article/doi/10.3934/math.20241672reinsurance and investmentvariance premium principlestochastic volatilityjoint exponential utility |
| spellingShingle | Wuyuan Jiang Zechao Miao Jun Liu Optimal investment and reinsurance for the insurer and reinsurer with the joint exponential utility AIMS Mathematics reinsurance and investment variance premium principle stochastic volatility joint exponential utility |
| title | Optimal investment and reinsurance for the insurer and reinsurer with the joint exponential utility |
| title_full | Optimal investment and reinsurance for the insurer and reinsurer with the joint exponential utility |
| title_fullStr | Optimal investment and reinsurance for the insurer and reinsurer with the joint exponential utility |
| title_full_unstemmed | Optimal investment and reinsurance for the insurer and reinsurer with the joint exponential utility |
| title_short | Optimal investment and reinsurance for the insurer and reinsurer with the joint exponential utility |
| title_sort | optimal investment and reinsurance for the insurer and reinsurer with the joint exponential utility |
| topic | reinsurance and investment variance premium principle stochastic volatility joint exponential utility |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241672 |
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