Optimal Investment and Reinsurance Policies in a Continuous-Time Model

Yan Tong, Tongling Lv and Yu Yan ()
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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

Mathematics, 2023, vol. 11, issue 24, 1-20

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.

Keywords: optimal investment; proportional reinsurance; jump–diffusion process; insurance company (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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