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Robust optimal control for an insurer with reinsurance and investment under Heston’s stochastic volatility model

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  • Yi, Bo
  • Li, Zhongfei
  • Viens, Frederi G.
  • Zeng, Yan

Abstract

This paper considers a robust optimal reinsurance and investment problem under Heston’s Stochastic Volatility (SV) model for an Ambiguity-Averse Insurer (AAI), who worries about model misspecification and aims to find robust optimal strategies. The surplus process of the insurer is assumed to follow a Brownian motion with drift. The financial market consists of one risk-free asset and one risky asset whose price process satisfies Heston’s SV model. By adopting the stochastic dynamic programming approach, closed-form expressions for the optimal strategies and the corresponding value functions are derived. Furthermore, a verification result and some technical conditions for a well-defined value function are provided. Finally, some of the model’s economic implications are analyzed by using numerical examples and simulations. We find that ignoring model uncertainty leads to significant utility loss for the AAI. Moreover we propose an alternative model and associated investment strategy which can be considered more adequate under certain finance interpretations, and which leads to significant improvements in our numerical example.

Suggested Citation

  • Yi, Bo & Li, Zhongfei & Viens, Frederi G. & Zeng, Yan, 2013. "Robust optimal control for an insurer with reinsurance and investment under Heston’s stochastic volatility model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 601-614.
  • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:601-614
    DOI: 10.1016/j.insmatheco.2013.08.011
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Chen, Lv & Qian, Linyi & Shen, Yang & Wang, Wei, 2016. "Constrained investment–reinsurance optimization with regime switching under variance premium principle," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 253-267.
    2. Gu, Ailing & Viens, Frederi G. & Yi, Bo, 2017. "Optimal reinsurance and investment strategies for insurers with mispricing and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 235-249.
    3. Zeng, Yan & Li, Danping & Gu, Ailing, 2016. "Robust equilibrium reinsurance-investment strategy for a mean–variance insurer in a model with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 138-152.
    4. Zhang, Xin & Meng, Hui & Zeng, Yan, 2016. "Optimal investment and reinsurance strategies for insurers with generalized mean–variance premium principle and no-short selling," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 125-132.
    5. repec:eee:insuma:v:80:y:2018:i:c:p:67-83 is not listed on IDEAS
    6. repec:spr:mathme:v:85:y:2017:i:2:d:10.1007_s00186-017-0570-8 is not listed on IDEAS
    7. Zheng, Xiaoxiao & Zhou, Jieming & Sun, Zhongyang, 2016. "Robust optimal portfolio and proportional reinsurance for an insurer under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 77-87.
    8. A, Chunxiang & Li, Zhongfei, 2015. "Optimal investment and excess-of-loss reinsurance problem with delay for an insurer under Heston’s SV model," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 181-196.
    9. Li, Bin & Li, Danping & Xiong, Dewen, 2016. "Alpha-robust mean-variance reinsurance-investment strategy," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 101-123.
    10. Shen, Yang & Zeng, Yan, 2015. "Optimal investment–reinsurance strategy for mean–variance insurers with square-root factor process," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 118-137.
    11. repec:eee:insuma:v:80:y:2018:i:c:p:93-109 is not listed on IDEAS
    12. Pun, Chi Seng & Wong, Hoi Ying, 2015. "Robust investment–reinsurance optimization with multiscale stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 245-256.
    13. Peng, Xingchun & Chen, Fenge & Hu, Yijun, 2014. "Optimal investment, consumption and proportional reinsurance under model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 222-234.
    14. repec:eee:dyncon:v:88:y:2018:i:c:p:70-103 is not listed on IDEAS
    15. Pun, Chi Seng & Wong, Hoi Ying, 2016. "Robust non-zero-sum stochastic differential reinsurance game," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 169-177.
    16. Bo Yi & Frederi Viens & Baron Law & Zhongfei Li, 2015. "Dynamic portfolio selection with mispricing and model ambiguity," Annals of Finance, Springer, vol. 11(1), pages 37-75, February.

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