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Optimal Investment and Reinsurance Policies in a Continuous-Time Model

Author

Listed:
  • Yan Tong

    (School of Mathematics and Science, Nankai University, No. 94 Weijin Road, Nankai District, Tianjin 300071, China)

  • Tongling Lv

    (School of Science, China Agricultural University, Haidian District, Beijing 100091, China)

  • Yu Yan

    (School of Economics, Peking University, Haidian District, Beijing 100871, China
    Key Laboratory of Mathematical Economics and Quantitative Finance, Peking University, Haidian District, Beijing 100871, China)

Abstract

In the field of finance and insurance, addressing the optimal investment and reinsurance issue is a focal point for researchers. This paper contemplates the optimal strategy for insurance companies within a model where wealth dynamics adhere to a jump–diffusion process. The fractional structure of the diffusion term is extremely interpretative. This model encompasses elements of risky assets, risk-free assets, and proportional reinsurance. Based on this model and grounded in the principles of stochastic control, the corresponding HJB equation is derived and solved. Consequently, explicit expressions for the optimal investment and reinsurance ratios are obtained, and the solution’s verification theorem is proven. Finally, through a numerical analysis with varying parameters, results consistent with real-world scenarios are achieved.

Suggested Citation

  • Yan Tong & Tongling Lv & Yu Yan, 2023. "Optimal Investment and Reinsurance Policies in a Continuous-Time Model," Mathematics, MDPI, vol. 11(24), pages 1-20, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:5005-:d:1302688
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    References listed on IDEAS

    as
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