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Robust optimal reinsurance and investment strategies for an AAI with multiple risks

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  • Guan, Guohui
  • Liang, Zongxia

Abstract

This paper studies the robust optimal reinsurance and investment problem for an ambiguity averse insurer (abbr. AAI). The AAI sells insurance contracts and has access to proportional reinsurance business. The AAI can invest in a financial market consisting of four assets: one risk-free asset, one bond, one inflation protected bond and one stock, and has different levels of ambiguity aversions towards the risks. The goal of the AAI is to seek the robust optimal reinsurance and investment strategies under the worst case scenario. Here, the nominal interest rate is characterized by the Vasicek model; the inflation index is introduced according to the Fisher’s equation; and the stock price is driven by the Heston’s stochastic volatility model. The explicit forms of the robust optimal strategies and value function are derived by introducing an auxiliary robust optimal control problem and stochastic dynamic programming method. In the end of this paper, a detailed sensitivity analysis is presented to show the effects of market parameters on the robust optimal reinsurance policy, the robust optimal investment strategy and the utility loss when ignoring ambiguity.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:89:y:2019:i:c:p:63-78
    DOI: 10.1016/j.insmatheco.2019.09.004
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    References listed on IDEAS

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    Cited by:

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    2. He, Yong & Luouyang, Xueqi & He, Lin & Chen, Haiyan & Li, Sheng, 2024. "Non-zero-sum investment-reinsurance game with delay and ambiguity aversion," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).
    3. Yuan, Yu & Han, Xia & Liang, Zhibin & Yuen, Kam Chuen, 2023. "Optimal reinsurance-investment strategy with thinning dependence and delay factors under mean-variance framework," European Journal of Operational Research, Elsevier, vol. 311(2), pages 581-595.
    4. Tong Qian & Cuixia Chen & Weijun Yin & Bing Liu, 2024. "Optimal Investment-reinsurance Strategies for an Insurer with Options Trading Under Model Ambiguity," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-21, December.
    5. Szymon Peszat & Dariusz Zawisza, 2020. "The investor problem based on the HJM model," Papers 2010.13915, arXiv.org, revised Dec 2021.
    6. 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.
    7. Park, Kyunghyun & Wong, Hoi Ying & Yan, Tingjin, 2023. "Robust retirement and life insurance with inflation risk and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 1-30.
    8. Guohui Guan & Jiaqi Hu & Zongxia Liang, 2021. "Robust equilibrium strategies in a defined benefit pension plan game," Papers 2103.09121, arXiv.org.

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    More about this item

    Keywords

    IE13; IE53; IM52; Robust optimal control; Proportional reinsurance; Investment; Stochastic inflation; Stochastic volatility;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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