Optimal Reinsurance–Investment Strategy Based on Stochastic Volatility and the Stochastic Interest Rate Model
This paper studies insurance companies’ optimal reinsurance–investment strategy under the stochastic interest rate and stochastic volatility model, taking the HARA utility function as the optimal criterion. It uses arithmetic Brownian motion as a diffusion approximation of the insurer’s surplus proc...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/8/736 |
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| author | Honghan Bei Qian Wang Yajie Wang Wenyang Wang Roberto Murcio |
| author_facet | Honghan Bei Qian Wang Yajie Wang Wenyang Wang Roberto Murcio |
| author_sort | Honghan Bei |
| collection | DOAJ |
| description | This paper studies insurance companies’ optimal reinsurance–investment strategy under the stochastic interest rate and stochastic volatility model, taking the HARA utility function as the optimal criterion. It uses arithmetic Brownian motion as a diffusion approximation of the insurer’s surplus process and the variance premium principle to calculate premiums. In this paper, we assume that insurance companies can invest in risk-free assets, risky assets, and zero-coupon bonds, where the Cox–Ingersoll–Ross model describes the dynamic change in stochastic interest rates and the Heston model describes the price process of risky assets. The analytic solution of the optimal reinsurance–investment strategy is deduced by employing related methods from the stochastic optimal control theory, the stochastic analysis theory, and the dynamic programming principle. Finally, the influence of model parameters on the optimal reinsurance–investment strategy is illustrated using numerical examples. |
| first_indexed | 2024-03-11T00:07:29Z |
| format | Article |
| id | doaj.art-6d6eb41687c64897987dfbaf3f532347 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T00:07:29Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-6d6eb41687c64897987dfbaf3f5323472023-11-19T00:14:26ZengMDPI AGAxioms2075-16802023-07-0112873610.3390/axioms12080736Optimal Reinsurance–Investment Strategy Based on Stochastic Volatility and the Stochastic Interest Rate ModelHonghan Bei0Qian Wang1Yajie Wang2Wenyang Wang3Roberto Murcio4School of Maritime Economics and Management, Dalian Maritime University, Dalian 116026, ChinaSchool of Maritime Economics and Management, Dalian Maritime University, Dalian 116026, ChinaSchool of Maritime Economics and Management, Dalian Maritime University, Dalian 116026, ChinaSchool of Maritime Economics and Management, Dalian Maritime University, Dalian 116026, ChinaDepartment of Geography, Birkbeck, London University, Malet Street, Bloomsbury, London WC1E 7HX, UKThis paper studies insurance companies’ optimal reinsurance–investment strategy under the stochastic interest rate and stochastic volatility model, taking the HARA utility function as the optimal criterion. It uses arithmetic Brownian motion as a diffusion approximation of the insurer’s surplus process and the variance premium principle to calculate premiums. In this paper, we assume that insurance companies can invest in risk-free assets, risky assets, and zero-coupon bonds, where the Cox–Ingersoll–Ross model describes the dynamic change in stochastic interest rates and the Heston model describes the price process of risky assets. The analytic solution of the optimal reinsurance–investment strategy is deduced by employing related methods from the stochastic optimal control theory, the stochastic analysis theory, and the dynamic programming principle. Finally, the influence of model parameters on the optimal reinsurance–investment strategy is illustrated using numerical examples.https://www.mdpi.com/2075-1680/12/8/736Cox–Ingersoll–Ross modelHeston modelvariance premium principleHARA utility |
| spellingShingle | Honghan Bei Qian Wang Yajie Wang Wenyang Wang Roberto Murcio Optimal Reinsurance–Investment Strategy Based on Stochastic Volatility and the Stochastic Interest Rate Model Axioms Cox–Ingersoll–Ross model Heston model variance premium principle HARA utility |
| title | Optimal Reinsurance–Investment Strategy Based on Stochastic Volatility and the Stochastic Interest Rate Model |
| title_full | Optimal Reinsurance–Investment Strategy Based on Stochastic Volatility and the Stochastic Interest Rate Model |
| title_fullStr | Optimal Reinsurance–Investment Strategy Based on Stochastic Volatility and the Stochastic Interest Rate Model |
| title_full_unstemmed | Optimal Reinsurance–Investment Strategy Based on Stochastic Volatility and the Stochastic Interest Rate Model |
| title_short | Optimal Reinsurance–Investment Strategy Based on Stochastic Volatility and the Stochastic Interest Rate Model |
| title_sort | optimal reinsurance investment strategy based on stochastic volatility and the stochastic interest rate model |
| topic | Cox–Ingersoll–Ross model Heston model variance premium principle HARA utility |
| url | https://www.mdpi.com/2075-1680/12/8/736 |
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