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Time-consistent reinsurance and investment strategies for mean–variance insurer under partial information

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  • Liang, Zongxia
  • Song, Min

Abstract

In this paper, based on equilibrium control law proposed by Björk and Murgoci (2010), we study an optimal investment and reinsurance problem under partial information for insurer with mean–variance utility, where insurer’s risk aversion varies over time. Instead of treating this time-inconsistent problem as pre-committed, we aim to find time-consistent equilibrium strategy within a game theoretic framework. In particular, proportional reinsurance, acquiring new business, investing in financial market are available in the market. The surplus process of insurer is depicted by classical Lundberg model, and the financial market consists of one risk free asset and one risky asset with unobservable Markov-modulated regime switching drift process. By using reduction technique and solving a generalized extended HJB equation, we derive closed-form time-consistent investment–reinsurance strategy and corresponding value function. Moreover, we compare results under partial information with optimal investment–reinsurance strategy when Markov chain is observable. Finally, some numerical illustrations and sensitivity analysis are provided.

Suggested Citation

  • Liang, Zongxia & Song, Min, 2015. "Time-consistent reinsurance and investment strategies for mean–variance insurer under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 66-76.
    • Handle: RePEc:eee:insuma:v:65:y:2015:i:c:p:66-76
    DOI: 10.1016/j.insmatheco.2015.08.008
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    References listed on IDEAS

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    Cited by:

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    2. Junna Bi & Jun Cai & Yan Zeng, 2021. "Equilibrium reinsurance-investment strategies with partial information and common shock dependence," Annals of Operations Research, Springer, vol. 307(1), pages 1-24, December.
    3. Van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2018. "Time-consistent mean–variance portfolio optimization: A numerical impulse control approach," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 9-28.
    4. Walter Mudzimbabwe, 2020. "A time consistent derivative strategy," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-25, March.
    5. Guohui Guan, 2020. "Equilibrium and Precommitment Mean-Variance Portfolio Selection Problem with Partially Observed Price Index and Multiple Assets," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 25-47, March.
    6. Wang, Hao & Wang, Rongming & Wei, Jiaqin, 2019. "Time-consistent investment-proportional reinsurance strategy with random coefficients for mean–variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 104-114.
    7. Xue, Xiaole & Wei, Pengyu & Weng, Chengguo, 2019. "Derivatives trading for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 40-53.
    8. Xie, Lin & Chen, Lv & Qian, Linyi & Li, Danping & Yang, Zhixin, 2023. "Optimal investment and consumption strategies for pooled annuity with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 129-155.
    9. Claudia Ceci & Katia Colaneri, 2024. "Portfolio and reinsurance optimization under unknown market price of risk," Papers 2408.07432, arXiv.org.
    10. Xue Dong He & Xun Yu Zhou, 2021. "Who Are I: Time Inconsistency and Intrapersonal Conflict and Reconciliation," Papers 2105.01829, arXiv.org.
    11. Haiying Zhou & Huainian Zhu, 2024. "Optimal Reinsurance and Derivative-Based Investment Decisions for Insurers with Mean-Variance Preference," Mathematics, MDPI, vol. 12(13), pages 1-20, June.
    12. Guan, Guohui & Liang, Zongxia, 2019. "Robust optimal reinsurance and investment strategies for an AAI with multiple risks," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 63-78.
    13. Zhang, Jingong & Tan, Ken Seng & Weng, Chengguo, 2017. "Optimal hedging with basis risk under mean–variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 1-15.
    14. Qiang Zhang & Qianqian Cui, 2024. "Robust Investment and Proportional Reinsurance Strategy with Delay and Jumps in a Stochastic Stackelberg Differential Game," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-34, December.
    15. van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2021. "The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors," European Journal of Operational Research, Elsevier, vol. 289(2), pages 774-792.

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    More about this item

    Keywords

    IE13; IE12; IM52; IB91; IE53; IE43; Equilibrium control law; Time-consistent strategy; Investment–reinsurance; Partial information; Mean–variance criterion; Regime switching;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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