Portfolio selection and risk control for an insurer with uncertain time horizon under inside information

Hongwei Liu; Xinzhi Wang; Caibo Xiao; Hongwei Liu; Xinzhi Wang; Caibo Xiao

doi:10.3934/math.2026451

AIMS Mathematics

2026, Volume 11, Issue 4: 10986-11011. doi: 10.3934/math.2026451

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Research article

Portfolio selection and risk control for an insurer with uncertain time horizon under inside information

1.
School of Mathematics and Computing Science, Guilin University of Electronic Technology, No. 1 Jinji Road, Guilin 541004, China
2.
School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, No. 1 Jinji Road, Guilin 541004, China
3.
Center for Applied Mathematics of Guangxi (GUET), No. 1 Jinji Road, Guilin 541004, China
4.
School of Humanities and Management, Guilin Medical University, Guilin 541199, China

Received: 24 December 2025 Revised: 03 April 2026 Accepted: 14 April 2026 Published: 20 April 2026
MSC : 91G80, 93E20

This paper is devoted to studying the optimal investment and risk control strategy for an insurer with uncertain time under inside information. The jump process is incorporated into our research framework, and the correlation between the risky asset and the risk process is considered. Assuming the exit time is uncertain, we use forward calculus and Malliavin calculus to derive a characterization of the optimal investment and risk control under the criterion of maximizing the logarithmic utility of the terminal wealth in a pure jump market and a mixed market. Moreover, we apply filtration enlargement techniques to several interesting special cases and derive the corresponding explicit solutions. Finally, we conduct numerical simulations to analyze the impact of correlation coefficient and insider information on the investment strategy.
- optimal strategy,
- random time,
- jump-diffusion model,
- inside information,
- Malliavin calculus
Citation: Hongwei Liu, Xinzhi Wang, Caibo Xiao. Portfolio selection and risk control for an insurer with uncertain time horizon under inside information[J]. AIMS Mathematics, 2026, 11(4): 10986-11011. doi: 10.3934/math.2026451

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Abstract

This paper is devoted to studying the optimal investment and risk control strategy for an insurer with uncertain time under inside information. The jump process is incorporated into our research framework, and the correlation between the risky asset and the risk process is considered. Assuming the exit time is uncertain, we use forward calculus and Malliavin calculus to derive a characterization of the optimal investment and risk control under the criterion of maximizing the logarithmic utility of the terminal wealth in a pure jump market and a mixed market. Moreover, we apply filtration enlargement techniques to several interesting special cases and derive the corresponding explicit solutions. Finally, we conduct numerical simulations to analyze the impact of correlation coefficient and insider information on the investment strategy.

References

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